Atomic and Nuclear Physics Review Material

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Review Material for a Physics Exam on Atomic and Nuclear Physics. Intended for International Baccalaureate students

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11.Which one of the following correctly gives the number of electrons, protons and neutrons in a neutral atom of the nuclide ?Number of electronsNumber of protonsNumber of neutronsA.652936B.363629C.292965D.292936(1) 2.In the Geiger-Marsden experiment, particles are scattered by gold nuclei. The experimental results indicate that most particles areA.scattered only at small angles.B.scattered only at large angles.C.absorbed in the target.D.scattered back along the original direction.(1) 3.A sample of radioactive carbon-14 decays into a stable isotope of nitrogen. As the carbon-14 decays, the rate at which the amount of nitrogen is producedA.decreases linearly with time.B.increases linearly with time.C.decreases exponentially with time.D.increases exponentially with time.(1)4.Either of the two following graphs is useful in predicting nuclear energy changes in fission and fusion processes. Which one of the following correctly identifies the quantities X and Y?XYA.atomic numbertotal binding energyB.mass numbertotal binding energyC.atomic numberaverage binding energy per nucleonD.mass numberaverage binding energy per nucleon(1) 5.The unified mass unit is defined asA.the mass of one neutral atom of C.B. of the mass of one neutral atom of C.C. of the mass of one neutral atom of C.D.the mass of the nucleus of C.(1)6.This question is about nuclear reactions.(a)Complete the table below, by placing a tick () in the relevant columns, to show how an increase in each of the following properties affects the rate of decay of a sample of radioactive material.PropertyEffect on rate of decayincreasedecreasestays the sametemperature of samplepressure on sampleamount of sample(2) Radium-226 (Ra) undergoes natural radioactive decay to disintegrate spontaneously with the emission of an alpha particle (-particle) to form radon (Rn). The masses of the particles involved in the reaction areradium:226.0254 uradon:222.0176 u-particle:4.0026 u(b)(i)Complete the nuclear reaction equation below for this reaction.Ra+Rn(2) (ii)Calculate the energy released in the reaction.............................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................(3)(c)The radium nucleus was stationary before the reaction.(i)Explain, in terms of the momentum of the particles, why the radon nucleus and the -particle move off in opposite directions after the reaction.............................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................(3) (ii)The speed of the radon nucleus after the reaction is vR and that of the -particle is v. Show that the ratio is equal to 55.5.............................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................(3) (iii)Using the ratio given in (ii) above, deduce that the kinetic energy of the radon nucleus is much less than the kinetic energy of the -particle...................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................(3)(d)Not all of the energy of the reaction is released as kinetic energy of the -particle and of the radon nucleus. Suggest one other form in which the energy is released......................................................................................................................................(1) Another type of nuclear reaction is a fusion reaction. This reaction is the main source of the Suns radiant energy.(e)(i)State what is meant by a fusion reaction.............................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................(3) (ii)Explain why the temperature and pressure of the gases in the Suns core must both be very high for it to produce its radiant energy.High temperature:................................................................................................................................................................................................................................................................................................................................................................................High pressure:................................................................................................................................................................................................................................................................................................................................................................................(5)(Total 25 marks)7.This question is about the production of nuclear energy and its transfer to electrical energy.(a)When a neutron collides with a nucleus of uranium-235 (U) the following reaction can occur.U+nBa+ Kr+ 2n(i)State the name given to this type of nuclear reaction............................................................................................................................(1) (ii)Energy is liberated in this reaction. In what form does this energy appear?...........................................................................................................................(1) (b)Describe how the neutrons produced in this reaction may initiate a chain reaction...........................................................................................................................................................................................................................................................................(1)The purpose of a nuclear power station is to produce electrical energy from nuclear energy. The diagram below is a schematic representation of the principle components of a nuclear reactor pile used in a certain type of nuclear power station.The function of the moderator is to slow down neutrons produced in a reaction such as that described in part (a) above.(c)(i)Explain why it is necessary to slow down the neutrons.............................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................(3) (ii)Explain the function of the control rods..................................................................................................................................................................................................................................................................................................................................................................................(2)(d)Describe briefly how the energy produced by the nuclear reactions is extracted from the reactor pile and then transferred to electrical energy...............................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................(4)(Total 12 marks) 8.This question is about nuclear reactions.(a)Complete the table below, by placing a tick () in the relevant columns, to show how an increase in each of the following properties affects the rate of decay of a sample of radioactive material.PropertyEffect on rate of decayincreasedecreasestays the sametemperature of samplepressure on sampleamount of sample(2)Radium-226 (Ra) undergoes natural radioactive decay to disintegrate spontaneously with the emission of an alpha particle (-particle) to form radon (Rn). The decay constant for this reaction is 4.30 104 yr1. The masses of the particles involved in the reaction areradium:226.0254 uradon:222.0176 u-particle:4.0026 u(b)(i)Explain what is meant by the statement that the decay constant is 4.30 104 yr1..................................................................................................................................................................................................................................................................................................................................................................................(2) (ii)Calculate the energy released in the reaction.............................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................(3) (c)The radium nucleus was stationary before the reaction.(i)Explain, in terms of the momentum of the particles, why the radon nucleus and the -particle move off in opposite directions after the reaction.............................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................(3) (ii)The speed of the radon nucleus after the reaction is vR and that of the -particle is v. Determine the ratio .............................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................(3) A college has been using a sample of radium-226 as an -particle source for 30 years. Initially, the mass of radium was 15.0 g.(d)Determine(i)the initial number of atoms of radium-226 in the sample;............................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................ (ii)the number of atoms of radium-226 in the sample after 30 years;............................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................ (iii)the average activity of the sample during the 30 year period.............................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................(6) (e)The -particle is composed of protons and neutrons. Describe, by reference to the structure of the proton and the neutron, why they are not classed as fundamental particles.....................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................(3) Another type of nuclear reaction is a fusion reaction. This reaction is the main source of the Suns radiant energy.(f)(i)State what is meant by a fusion reaction.............................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................(3) (ii)Explain why the temperature and pressure of the gases in the Suns core must both be very high for it to produce its radiant energy.High temperature:................................................................................................................................................................................................................................................................................................................................................................................ High pressure:................................................................................................................................................................................................................................................................................................................................................................................(5)(Total 30 marks)9.Which one of the following provides direct evidence for the existence of discrete energy levels in an atom?A.The continuous spectrum of the light emitted by a white-hot metal.B.The line emission spectrum of a gas at low pressure.C.The emission of gamma radiation from radioactive atoms.D.The ionization of gas atoms when bombarded by alpha particles.(1) 10.A sample of material initially contains atoms of only one radioactive isotope. Which one of the following quantities is reduced to one half of its initial value during a time equal to the half-life of the radioactive isotope?A.Total mass of the sampleB.Total number of atoms in the sampleC.Total number of nuclei in the sampleD.Activity of the radioactive isotope in the sample(1) 11.In a fission chain reaction,A.energy from one fission reaction causes further fission reactions.B.nuclei produced in one fission reaction cause further fission reactions.C.neutrons from one fission reaction cause further fission reactions.D.gamma radiation produced in one fission reaction causes further fission reactions.(1)12.This question is about atomic and nuclear structure.In a nuclear model of the atom, most of the atom is regarded as empty space. A tiny nucleus is surrounded by a number of electrons.(a)Outline one piece of experimental evidence that supports this nuclear model of the atom...............................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................(3) (b)Explain why the protons in a nucleus do not fly apart from each other.....................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................(2)(c)In total, there are approximately 1029 electrons in the atoms making up a person.(i)Estimate the electrostatic force of repulsion between two people standing 100 m apart as a result of these electrons.........................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................(4) (ii)Explain why two people standing 100 m apart would not feel the force that you have calculated in part (i).............................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................(2)(Total 11 marks)13.The variation with thickness x of the number n of -particles penetrating a material is shown below. What can be deduced from the graph about the -particles?A.The -particles have approximately the same initial energy.B.The range is independent of the initial energy.C.The -particles produce high levels of ionization.D.The -particles have a large mass.(1) 14.K-capture is a process that occurs when a nucleus captures an electron from the innermost shell of electrons surrounding the nucleus.When K-capture occurs in iron-55 (Fe), the nucleus is changed into a manganese (Mn) nucleus. Which equation represents this change?A.(Fe) + e MnB.(Fe) +e MnC.(Fe) +e MnD.(Fe) +e Mn(1) 15.This question is about atomic and nuclear structure and fundamental forces.In a nuclear model of the atom, most of the atom is regarded as empty space. A tiny nucleus is surrounded by a number of electrons.(a)Outline one piece of experimental evidence that supports this nuclear model of the atom...............................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................(3) (b)Explain why the protons in a nucleus do not fly apart from each other.....................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................(2)(c)In total, there are approximately 1029 electrons in the atoms making up a person. Estimate the electrostatic force of repulsion between two people standing 100 m apart as a result of these electrons.........................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................(4) (d)Estimate the gravitational force of attraction between two people standing 100 m apart.....................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................(2) (e)Explain why two people standing 100 m apart would not feel either of the forces that you have calculated in parts (c) and (d).....................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................(2)(Total 13 marks)16.This question considers some aspects of the atomic and nuclear physics associated with isotopes of the element helium.Atomic aspects(a)The element helium was first identified from the absorption spectrum of the Sun.(i)Explain what is meant by the term absorption spectrum..................................................................................................................................................................................................................................................................................................................................................................................(2) (ii)Outline how this spectrum may be experimentally observed..................................................................................................................................................................................................................................................................................................................................................................................(2)(b)One of the wavelengths in the absorption spectrum of helium occurs at 588 nm.(i)Show that the energy of a photon of wavelength 588 nm is 3.38 1019 J.............................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................(2) (ii)The diagram below represents some of the energy levels of the helium atom. Use the information in the diagram to explain how absorption at 588 nm arises........................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................(3)Two different models have been developed to explain the existence of atomic energy levels. The Bohr model and the Schrdinger model are both able to predict the principal wavelengths present in the spectrum of atomic hydrogen.(c)Outline(i)the Bohr model, and(ii)the Schrdinger model...............................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................(6)Nuclear aspects(d)The helium in the Sun is produced as a result of a nuclear reaction. Explain whether this reaction is burning, fission or fusion.....................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................(2) At a later stage in the development of the Sun, other nuclear reactions are expected to take place. One such overall reaction is given below.He + He +He C + +(e)(i)Identify the atomic number and the mass number of the isotope of carbon C that has been formed.Atomic number: ...Mass number: ...(2) (ii)Use the information below to calculate the energy released in the reaction.Atomic mass of helium = 6.648 325 1027 kgAtomic mass of carbon = 1.993 200 1026 kg.......................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................(3)Another isotope of helium He decays by emitting a -particle.(f)(i)State the name of the other particle that is emitted during this decay............................................................................................................................(1) (ii)Explain why a sample of He emits -particles with a range of energies..................................................................................................................................................................................................................................................................................................................................................................................(2) (iii)The half-life for this decay is 0.82 s. Determine the percentage of a sample of He that remains after a time of 10 s...................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................(3) (iv)Describe the process of decay in terms of quarks..................................................................................................................................................................................................................................................................................................................................................................................(2)(Total 30 marks)17.This question is about the Bohr model of the hydrogen atom and the Heisenberg uncertainty principle.(a)A postulate of the Bohr model of the hydrogen atom is that the electron revolves about the proton in stable, circular orbits. State two other postulates of the Bohr model.1 ....................................................................................................................................................................................................................................................................2 ......................................................................................................................................................................................................................................................................................................................................................................................................(2) In the nth energy state, the hydrogen atom has energy En and the electron orbits with speed vn in an orbit of radius rn. En, rn and vn are given by the following relationships.En = eVrn = 0.0529n2 nmvn = m s1 (b)Apply the expressions above, to hydrogen in its ground state, to determine the ground state energy, the radius of the electron orbit and the electron speed.....................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................(2)(c)According to the Schrdinger model, the position and the speed of an electron are not well defined. It can be assumed that the uncertainty in the position of the electron in a hydrogen atom is equal to the radius of the electron orbit in the n = 1 state.(i)Apply the Heisenberg uncertainty principle to hydrogen in this state to show that the uncertainty in the speed of the electron is approximately equal to the electron speed as calculated in (b)...................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................(3) (ii)Explain why the result in (i) above suggests that the idea of electron orbits, as used in the Bohr model, is a poor one........................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................(3)(Total 10 marks)18.Which one of the following correctly identifies the atomic (proton) number and mass (nucleon) number of a nucleus that has neutrons n and protons p?Atomic numberMass numberA.pnB.pn + pC.npD.n + pp(1) 19.In a laboratory when aluminium nuclei are bombarded with -particles, the following reaction may take place.This reaction is an example ofA.nuclear fission.B.nuclear fusion.C.natural radioactive decay.D.artificial transmutation.(1) 20.Isotopes provide evidence for the existence ofA.protons.B.electrons.C.nuclei.D.neutrons.(1) 21.This question is about nuclear reactions.(a)(i)Distinguish between fission and radioactive decay........................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................(4) A nucleus of uranium-235 () may absorb a neutron and then undergo fission to produce nuclei of strontium-90 () and xenon-142 () and some neutrons.The strontium-90 and the xenon-142 nuclei both undergo radioactive decay with the emission of particles.(ii)Write down the nuclear equation for this fission reaction.......................................................................................................................................................................................................................................................(2) (iii)State the effect, if any, on the mass number (nucleon number) and on the atomic number (proton number) of a nucleus when the nucleus undergoes decay.Mass number: ...................................................................................................Atomic number: ...............................................................................................(2)The uranium-235 nucleus is stationary at the time that the fission reaction occurs. In this fission reaction, 198 MeV of energy is released. Of this total energy, 102 MeV and 65 MeV are the kinetic energies of the strontium-90 and xenon-142 nuclei respectively.(b)(i)Calculate the magnitude of the momentum of the strontium-90 nucleus.............................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................(4) (ii)Explain why the magnitude of the momentum of the strontium-90 nucleus is not exactly equal in magnitude to that of the xenon-142 nucleus.............................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................(2) On the diagram below, the circle represents the position of a uranium-235 nucleus before fission. The momentum of the strontium-90 nucleus after fission is represented by the arrow. (iii)On the diagram above, draw an arrow to represent the momentum of the xenon-142 nucleus after the fission.(2)(c)In a fission reactor for the generation of electrical energy, 25% of the total energy released in a fission reaction is converted into electrical energy.(i)Using the data in (b), calculate the electrical energy, in joules, produced as a result of nuclear fission of one nucleus..................................................................................................................................................................................................................................................................................................................................................................................(2) (ii)The specific heat capacity of water is 4.2 103 J Kg1 K1. Calculate the energy required to raise the temperature of 250 g of water from 20C to its boiling point (100C)..................................................................................................................................................................................................................................................................................................................................................................................(3) (iii)Using your answer to (c)(i), determine the mass of uranium-235 that must be fissioned in order to supply the amount of energy calculated in (c)(ii). The mass of a uranium-235 atom is 3.9 1025 kg........................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................(4)(Total 25 marks)22.This question is about nuclear reactions.(a)(i)Distinguish between fission and radioactive decay........................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................(4) A nucleus of uranium-235 () may absorb a neutron and then undergo fission to produce nuclei of strontium-90 () and xenon-142 () and some neutrons.The strontium-90 and the xenon-142 nuclei both undergo radioactive decay with the emission of particles.(ii)Write down the nuclear equation for this fission reaction.......................................................................................................................................................................................................................................................(2) (iii)State the effect, if any, on the mass number (nucleon number) and on the atomic number (proton number) of a nucleus when the nucleus undergoes decay.Mass number: ...................................................................................................Atomic number: ................................................................................................(2)The uranium-235 nucleus is stationary at the time that the fission reaction occurs. In this fission reaction, 198 MeV of energy is released. Of this total energy, 102 MeV and 65 MeV are the kinetic energies of the strontium-90 and xenon-142 nuclei respectively.(b)(i)Suggest what has happened to the remaining 31 MeV of energy..................................................................................................................................................................................................................................................................................................................................................................................(2) (ii)Calculate the magnitude of the momentum of the strontium-90 nucleus.............................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................(4) (iii)Explain why the magnitude of the momentum of the strontium-90 nucleus is not exactly equal in magnitude to that of the xenon-142 nucleus.............................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................(2) On the diagram below, the circle represents the position of a uranium-235 nucleus before fission. The momentum of the strontium-90 nucleus after fission is represented by the arrow. (iv)On the diagram above, draw an arrow to represent the momentum of the xenon-142 nucleus after the fission.(2) (c)(i)Define the decay constant for radioactive decay..................................................................................................................................................................................................................................................................................................................................................................................(2) (ii)The half-life of strontium-90 is 28.0 years. Deduce that the decay constant of strontium-90 is 7.85 1010 s1.......................................................................................................................................................................................................................................................(1) (d)The decay constant of xenon-142 is 0.462 s1. Initially, a sample of radioactive waste material contains equal numbers of strontium-90 and xenon-142 nuclei.(i)Use the values of the decay constants in (c) and (d) to calculate the time taken for the ratioto become equal to 1.20 106.............................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................(3)(ii)Suggest why, in the long-term, strontium-90 presents a greater problem then xenon-142 as radioactive waste..................................................................................................................................................................................................................................................................................................................................................................................(2)(Total 26 marks) 23.This question is about atomic models.The Bohr model was developed in order to explain the atomic spectrum of hydrogen.(a)Explain how the Bohr model was used to explain the spectrum of atomic hydrogen...............................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................(4) (b)State one limitation of the Bohr model.....................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................(1)A later model of the atom was developed by Schrdinger.(c)(i)State two differences between the model of Bohr and the model of Schrdinger.............................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................(2) (ii)Explain how the Schrdinger theory is consistent with the Heisenberg uncertainty principle.............................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................(3)(Total 10 marks) 24.An isotope of radium has a half-life of 4 days. A freshly prepared sample of this isotope contains N atoms. The time taken for of the atoms of this isotope to decay isA.32 days.B.16 days.C.12 days.D.8 days.(1)25.The presence of neutrons inside the nucleus is supported by the existence ofA.isotopes.B.orbiting electrons.C.gamma radiation.D.neutral atoms.(1) 26.The source of the Suns energy isA.fission.B.radioactivity.C.fusion.D.ionization.(1) 27.This question is about nuclear binding energy.(a)(i)Define nucleon............................................................................................................................(1)(ii)Define nuclear binding energy of a nucleus.......................................................................................................................................................................................................................................................(1)The axes below show values of nucleon number A (horizontal axis) and average binding energy per nucleon E (vertical axis). (Binding energy is taken to be a positive quantity). (b)Mark on the E axis above, the approximate position of(i)the isotope (label this F).(1) (ii)the isotope (label this H).(1) (iii)the isotope (label this U).(1) (c)Using the grid in part (a), draw a graph to show the variation with nucleon number A of the average binding energy per nucleon E.(2) (d)Use the following data to deduce that the binding energy per nucleon of the isotope is 2.2 MeV.nuclear mass of = 3.01603 umass of proton= 1.00728 umass of neutron= 1.00867 u.........................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................(3) In the nuclear reaction energy is released.(e)(i)State the name of this type of reaction............................................................................................................................(1) (ii)Use your graph in (c) to explain why energy is released in this reaction..................................................................................................................................................................................................................................................................................................................................................................................(2)(Total 13 marks) 28.This question is about nuclear binding energy.(a)Define nuclear binding energy...........................................................................................................................................................................................................................................................................(1)The axes below show values of nucleon number A (horizontal axis) and average binding energy per nucleon E (vertical axis). (Binding energy is taken to be a positive quantity). (b)Mark on the E axis opposite, the approximate position of(i)the isotope (label this F).(1)(ii)the isotope (label this H).(1)(iii)the isotope (label this U).(1) (c)Using the grid opposite, draw a graph to show the variation with nucleon number A of the average binding energy per nucleon E.(2)(d)Use the following data to deduce that the binding energy per nucleon of the isotope is 2.2MeV.nuclear mass of = 3.01603 umass of proton= 1.00728 umass of neutron= 1.00867 u.........................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................(3) In the nuclear reaction + He + energy is released.(e)(i)State the name of this type of reaction............................................................................................................................(1) (ii)Use your graph in (e) to explain why energy is released in this reaction..................................................................................................................................................................................................................................................................................................................................................................................(2)(Total 12 marks)29.This question is about the nuclear structure of the atom and atomic energy levels.When the electron was first discovered it led to the idea that an atom consists of a lump of positive charge in which the electrons are embedded.In 1912 Geiger and Marsden carried out an experiment to test the validity of this idea. The results of their experiment in fact suggested that the atom is mostly empty space with an electrically charged nucleus of relatively large mass occupying only a small amount of space. (This is the so-called nuclear model of the atom). Their experiment involved firing alpha particles at a thin sheet of gold foil.(a)State the nature of an alpha particle......................................................................................................................................(1) The diagram below shows a small part of the gold foil with two alpha particles A and B approaching the foil. (b)(i)Some alpha particle trajectories lead to the idea that most of the atom is empty space. On the diagram, draw such a trajectory for the alpha particle A.(1)(ii)Some other alpha particle trajectories lead to the idea that the atom has an electrically charged, relatively massive nucleus. On the diagram, draw such a trajectory for the alpha particle B.(1) (iii)Describe briefly how these trajectories lead to the idea of the nuclear model of the atom........................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................(4) In 1914 Niels Bohr suggested that the electrons in an hydrogen atom occupy discrete energy levels. The diagram below shows some of the principal energy levels. (c)(i)Label with the letter X, the energy level in which an electron will have zero potential energy.(1) (ii)Explain how the line spectra of atomic hydrogen supports the idea of discrete energy levels. You may use the diagram above to support your answer...................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................(4)(Total 12 marks) 30.In an -particle scattering experiment (Geiger-Marsden experiment), the number n of particles incident per unit time on a detector was determined for different angles of deflection .Which of the following graphs best shows the variation with of n?(1)31.The existence of isotopes provides evidence for the presence ofA.electrons in atomic energy levels.B.electrons in the nuclei of atoms.C.neutrons in the nuclei of atoms.D.protons in the nuclei of atoms.(1) 32.When a high-energy -particle collides with an aluminium-27 () nucleus, a nucleus of phosphorus may be produced. Which of the following equations correctly shows this transmutation?A.B.C.D.(1) 33.This question is about radioactivity and nuclear energy.(a)Define the following terms,(i)Isotope......................................................................................................................................................................................................................................................(1)(ii)Radioactive half-life......................................................................................................................................................................................................................................................(1) Thorium-227 (Th-227) results from the decay of the isotope actinium-227.(b)(i)Complete the following reaction equation.(1) Th-227 has a half-life of 18 days and undergoes a-decay to the isotope Ra-223 (Ra-223). A sample of Th-227 has an initial activity of 32 arbitrary units.(ii)Using the axes below, draw a graph to show the variation with time t (for t = 0 to t= 72 days) of the activity A of Th-227.(2)(iii)Determine from your graph, the activity of thorium after 50 days............................................................................................................................(1) (iv)Outline the experimental procedure to measure the activity of Th-227.............................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................(2) In the decay of a Th-227 nucleus, a -ray photon is also emitted.(c)Use the following data to deduce that the energy of the -ray photon is 0.667 MeV.mass of Th-227 nucleus= 227.0278 umass of Ra-223 nucleus= 223.0186 umass of helium nucleus= 4.0026 uenergy of -particle emitted=5.481 MeVunified atomic mass unit (u)= 931.5 MeV c2You may assume that the Th-227 nucleus is stationary before decay and that the Ra-223 nucleus has negligible kinetic energy..........................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................(3)(Total 11 marks)34.Ag-102, Ag-103 and Ag-104 are three isotopes of the element silver.Which one of the following is a true statement about the nuclei of these isotopes?A.All have the same mass.B.All have the same number of nucleons.C.All have the same number of neutrons.D.All have the same number of protons.(1) 35.Radioactive decay is a random process. This means thatA.a radioactive sample will decay continuously.B.some nuclei will decay faster than others.C.it cannot be predicted how much energy will be released.D.it cannot be predicted when a particular nucleus will decay.(1) 36.A freshly-prepared sample of cobalt-64 () decays by the emission of -ray photons. The decay may be represented by the nuclear equation+ energy.After this decay, the binding energy per nucleon hasA.increased in magnitude because energy has been emitted from the nucleus.B.decreased in magnitude because energy has been emitted from the nucleus.C.stayed constant because the number of nucleons in the nucleus is unchanged.D.stayed constant because the proton number is unchanged.(1)37.This question is about momentum and the kinematics of a proposed journey to Jupiter.(a)State the law of conservation of momentum................................................................................................................................................................................................................................................................................................................................................................................................................(2) A solar propulsion engine uses solar power to ionize atoms of xenon and to accelerate them. As a result of the acceleration process, the ions are ejected from the spaceship with a speed of 3.0104 m s1. (b)The mass (nucleon) number of the xenon used is 131. Deduce that the mass of one ion of xenon is 2.2 1025 kg.....................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................(2) (c)The original mass of the fuel is 81 kg. Deduce that, if the engine ejects 77 1018 xenon ions every second, the fuel will last for 1.5 years. (1 year = 3.2 107 s)....................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................(2)(d)The mass of the spaceship is 5.4 102 kg. Deduce that the initial acceleration of the spaceship is 8.2 105 m s2...............................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................(5) The graph below shows the variation with time t of the acceleration a of the spaceship. The solar propulsion engine is switched on at time t = 0 when the speed of the spaceship is 1.2103 m s1.(e)Explain why the acceleration of the spaceship is increasing with time.....................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................(2) (f)Using data from the graph, calculate the speed of the spaceship at the time when the xenon fuel has all been used..........................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................(4) (g)The distance of the spaceship from Earth when the solar propulsion engine is switched on is very small compared to the distance from Earth to Jupiter. The fuel runs out when the spaceship is a distance of 4.7 1011 m from Jupiter. Estimate the total time that it would take the spaceship to travel from Earth to Jupiter.....................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................(2)(Total 19 marks)38.This question is about radioactive decay.A nucleus of the isotope xenon, Xe-131, is produced when a nucleus of the radioactive isotope iodine I-131 decays.(a)Explain the term isotopes................................................................................................................................................................................................................................................................................................................................................................................................................(2) (b)Fill in the boxes below in order to complete the nuclear reaction equation for this decay.(2) (c)The activity A of a freshly prepared sample of the iodine isotope is 3.2 105 Bq. The variation of the activity A with time t is shown below.Draw a best-fit line for the data points.(1)(d)Use the graph to estimate the half-life of I-131......................................................................................................................................(1)(Total 6 marks) 39.This question is about atomic models. The diagram below (not to scale) shows a simple model of the hydrogen atom in which the electron orbits the proton in a circular path of radius R. (a)On the diagram, draw an arrow to show the direction of(i)the acceleration of the electron (label this A);(1)(ii)the velocity of the electron (label this V).(1) (b)State an expression for the magnitude of the electrostatic force F acting on the electron...........................................................................................................................................................................................................................................................................(1)(c)The orbital speed of the electron is 2.2 106 m s1.Deduce that the radius R of the orbit is 5.2 1011 m...............................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................(3) (d)A more complex model of the atom suggests that the orbital radius can only take certain discrete values. This leads to the idea of discrete energy levels within the atom. Outline the evidence that supports the existence of discrete energy levels.........................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................(3)(Total 9 marks)40.The number of nucleons in a nucleus is the number ofA.particles in the nucleus.B.neutrons in the nucleus.C.protons in the nucleus.D.protons plus neutrons in the nucleus.(1) 41.This question is about radioactive decay.A nucleus of the isotope xenon, Xe-131, is produced when a nucleus of the radioactive isotope iodine I-13 decays.(a)Explain the term isotopes................................................................................................................................................................................................................................................................................................................................................................................................................(2) (b)Fill in the boxes below in order to complete the nuclear reaction equation for this decay.(2)The activity A of a freshly prepared sample of the iodine isotope is 6.4 105 Bq and its half-life is 8.0 days.(c)Using the axes, draw a graph to illustrate the decay of this sample.(3) (d)Determine the decay constant of the isotope I-131....................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................(2)The sample is to be used to treat a growth in the thyroid of a patient. The isotope should not be used until its activity is equal to 0.5 105 Bq.(e)Calculate the time it takes for the activity of a freshly prepared sample to be reduced to an activity of 0.5 105 Bq....................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................(2)(Total 11 marks) 42.The emission and absorption spectra of different elements provides evidence for the existence ofA.isotopes.B.neutrons.C.protons.D.atomic energy levels.(1) 43.The nucleus of an atom contains protons. The protons are prevented from flying apart byA.the presence of orbiting electrons.B.the presence of gravitational forces.C.the presence of strong attractive nuclear forces.D.the absence of Coulomb repulsive forces at nuclear distances.(1)44.Which of the following gives the correct number of protons and number of neutrons in the nucleus of Number of protonsNumber of neutronsA.56B.511C.65D.115(1) 45.The unified mass unit is defined as the rest mass ofA.a proton.B.an atom of carbon-12 divided by 12.C.an atom of carbon-12.D.an atom of hydrogen-1.(1) 46.This question is about collisions and radioactive decay.(a)(i)Define linear momentum and impulse.Linear momentum:....................................................................................................................................................................................Impulse:....................................................................................................................................................................................(2)(ii)State the law of conservation of momentum..................................................................................................................................................................................................................................................................................................................................................................................(2) (iii)Using your definitions in (a)(i), deduce that linear momentum is constant for an object in equilibrium.............................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................(2) A stationary radon-220 () nucleus undergoes -decay to form a nucleus of polonium (Po). The -particle has kinetic energy of 6.29 MeV.(b)(i)Complete the nuclear equation for this decay.Po+(2) (ii)Calculate the kinetic energy, in joules, of the -particle.......................................................................................................................................................................................................................................................(2) (iii)Deduce that the speed of the -particle is 1.74 107 m s1..................................................................................................................................................................................................................................................................................................................................................................................(1) The diagram below shows the -particle and the polonium nucleus immediately after the decay. The direction of the velocity of the -particle is indicated. (c)(i)On the diagram above, draw an arrow to show the initial direction of motion of the polonium nucleus immediately after the decay.(1) (ii)Determine the speed of the polonium nucleus immediately after the decay.............................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................(3) (iii)In the decay of another radon nucleus, the nucleus is moving before the decay. Without any further calculation, suggest the effect, if any, of this initial speed on the paths shown in (c)(i)..................................................................................................................................................................................................................................................................................................................................................................................(2) The half-life of the decay of radon-220 is 55 s.(d)(i)Explain why it is not possible to state a time for the life of a radon-220 nucleus..................................................................................................................................................................................................................................................................................................................................................................................(2)(ii)Define half-life..................................................................................................................................................................................................................................................................................................................................................................................(2) A sample of radon-220 has an initial activity A0.(iii)On the axes below, draw a graph to show the variation with time t of the activity A for time t = 0 to time t = 180 s.(2)(iv)Use your graph to determine the activity, in terms of A0, of the sample of radon at time t = 120 s. Also, estimate the activity, in terms of A0, at time t = 330 s.Activity at time t = 120 s : ................................................Activity at time t = 330 s : ............................................(2)(Total 25 marks) 47.The graph below shows the variation with mass (nucleon) number of the average binding energy per nucleon. Which direction indicates a fission reaction with a release of energy?A.IB.IIC.IIID.IV(1)48.This question is about nuclear fission and nuclear fusion.(a)Compare the processes of nuclear fission and nuclear fusion..........................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................(4) (b)A nuclear fusion reaction that is being investigated for the production of power iswhere the energy liberated in each reaction is Determine the rate, in kg s1, of production of required for a power output of 100MW................................................................................................................................................................................................................................................................................................................................................................................................................(2)(Total 6 marks) 49.This question is about collisions and radioactive decay.(a)(i)Define linear momentum and impulse.Linear momentum:....................................................................................................................................................................................Impulse:....................................................................................................................................................................................(2)(ii)State the law of conservation of momentum..................................................................................................................................................................................................................................................................................................................................................................................(2) (iii)Using your definitions in (a)(i), deduce that linear momentum is constant for an object in equilibrium.............................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................(2) A stationary radon-220 () nucleus undergoes -decay to form a nucleus of polonium (Po). The -particle has kinetic energy of 6.29 MeV.(b)(i)Complete the nuclear equation for this decay.Po+(2) (ii)Calculate the kinetic energy, in joules, of the -particle.......................................................................................................................................................................................................................................................(2) (iii)Deduce that the speed of the -particle is 1.74 107 m s1..................................................................................................................................................................................................................................................................................................................................................................................(1) The diagram below shows the -particle and the polonium nucleus immediately after the decay. The direction of the velocity of the -particle is indicated. (c)(i)On the diagram above, draw an arrow to show the initial direction of motion of the polonium nucleus immediately after the decay.(1) (ii)Determine the speed of the polonium nucleus immediately after the decay.............................................................................................................................................................................................................................................................................................................................................................................................................................................................................................................(3) (iii)In the decay of another radon nucleus, the nucleus is moving before the decay. Without any further calculation, suggest the effect, if any, of this initial speed on the paths shown in (c)(i)..................................................................................................................................................................................................................................................................................................................................................................................(2)The half-life of the decay of radon-222 is 3.8 days and radon-220 has a half-life of 55 s.(d)(i)Suggest three ways in which nuclei of radon-222 differ from those of radon-220.1...................................................................................................................................................................................................................................2.....................................................................................................