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9702/04/M/J/09 UCLES 2009
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1. (a) A sample of a radioactive isotope contains N nuclei at time t. At time (t + t), it contains (N N) nuclei of the isotope.
For the period t, state, in terms of N, N and t,
(i) the mean activity of the sample,
activity =
(ii) the probability of decay of a nucleus.
probability =
(b) A cobalt-60 source having a half-life of 5.27 years is calibrated and found to have an activity of 3.50 105 Bq. The uncertainty in the calibration is 2%.
Calculate the length of time, in days, after the calibration has been made, for the stated activity of 3.50 105 Bq to have a maximum possible error of 10%.
By: N.A Rasih G3 Page 1 of 17 2/7/2011
norashikinText Boxsource must decay by 8% C1A = A0 exp(ln2 t / T) or A/ A0 = 1 / (2t/T) C10.92 = exp(ln2 t / 5.27) or 0.92 = 1 / (2t/5.27) C1 t = 0.634 years = 230 days A1(allow 2 marks for A/ A0 = 0.08, answer 7010 daysallow 1 mark for A/ A0 = 0.12, answer 5880 days)
norashikinText BoxN / t (ignore any sign) B1 [1]
norashikinText BoxN / N (ignore any sign) B1 [1]
9702/41/M/J/10 UCLES 2010
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2. A 0 meson is a sub-atomic particle. A stationary 0 meson, which has mass 2.4 1028 kg, decays to form two -ray photons. The nuclear equation for this decay is
0 + .
(a) Explain why the two -ray photons have the same energy.
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(b) Determine, for each -ray photon,
(i) the energy, in joule,
(ii) the wavelength,
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(iii) the momentum.
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3. Americium-241 is an artificially produced radioactive element that emits -particles. A sample of americium-241 of mass 5.1 g is found to have an activity of 5.9 105 Bq.
(a) Determine, for this sample of americium-241,
(i) the number of nuclei,
(ii) the decay constant,
(iii) the half-life, in years.
(b) Another radioactive element has a half-life of approximately 4 hours. Suggest why measurement of the mass and activity of a sample of this element is not
appropriate for the determination of its half-life.
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9702/41/O/N/09 UCLES 2009
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4. The controlled reaction between deuterium(2 1 H) and tritium(31 H) has involved ongoing research for many years. The reaction may be summarised as
21
H + 31
H 42He + 10
n + Q
where Q = 17.7 MeV.
Binding energies per nucleon are shown in Fig. 8.1.
binding energy per nucleon/ MeV
21 H
10 n
42He
1.12
7.07
Fig. 8.1
(a) Suggest why binding energy per nucleon for the neutron is not quoted. ..........................................................................................................................................
(b) Calculate the mass defect, in kg, of a helium 4 2He nucleus.
(c) (i) State the name of the type of reaction illustrated by this nuclear equation. ............................................................................................................................ [1]
(ii) Determine the binding energy per nucleon, in MeV, of tritium (31
H).
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9702/42/O/N/09 UCLES 2009
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5. (a) State what is meant by the decay constant of a radioactive isotope.
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(b) Show that the decay constant is related to the half-life t 12 by the expression
t 12 = 0.693.
[
(c) Cobalt-60 is a radioactive isotope with a half-life of 5.26 years (1.66 108 s).
A cobalt-60 source for use in a school laboratory has an activity of 1.8 105 Bq.
Calculate the mass of cobalt-60 in the source.
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9702/04/M/J/05
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UCLES 20056.
6 The isotope Manganese-56 decays and undergoes -particle emission to form the stableisotope Iron-56. The half-life for this decay is 2.6 hours.Initially, at time t = 0, a sample of Manganese-56 has a mass of 1.4g and there is no Iron-56.
(a) Complete Fig. 7.1 to show the variation with time t of the mass of Iron-56 in the samplefor time t = 0 to time t = 11 hours.
[Fig. 7.1
(b) For the sample of Manganese-56, determine
(i) the initial number of Manganese-56 atoms in the sample,
(ii) the initial activity.
0 2 4 6 8 10 12
mass ofIron-56
t / hours
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(c) Determine the time at which the ratio
is equal to 9.0.
t
mass of Iron-56mass of Manganese-56
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UCLES 2005
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9702/04/M/J/07
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UCLES 2007
7. (a) Define the decay constant of a radioactive isotope.
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(b) Strontium-90 is a radioactive isotope having a half-life of 28.0 years. Strontium-90 has a density of 2.54 g cm3.
A sample of Strontium-90 has an activity of 6.4 109 Bq. Calculate
(i) the decay constant , in s1, of Strontium-90,
(ii) the mass of Strontium-90 in the sample,
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UCLES 2007
(iii) the volume of the sample.
(c) By reference to your answer in (b)(iii), suggest why dust that has been contaminated with Strontium-90 presents a serious health hazard.
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9702/04/M/J/08
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UCLES 2008
8 A positron ( 0+1e ) is a particle that has the same mass as an electron and has a charge of +1.6 1019 C.
A positron will interact with an electron to form two -ray photons.
0+1e +
01e 2
Assuming that the kinetic energy of the positron and the electron is negligible when they interact,
(a) suggest why the two photons will move off in opposite directions with equal energies,
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(b) calculate the energy, in MeV, of one of the -ray photons.
energy = ........................................... MeV [3]
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9702/04/O/N/05
8. Fig. 7.1 illustrates the variation with nucleon number A of the binding energy per nucleon Eof nuclei.
Fig. 7.1
(a) (i) Explain what is meant by the binding energy of a nucleus.
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(ii) On Fig. 7.1, mark with the letter S the region of the graph representing nucleihaving the greatest stability.
(b) Uranium-235 may undergo fission when bombarded by a neutron to produce
n Xenon-142 and Strontium-90 as shown below.
U + n Xe + Sr + neutrons
(i) Determine the number of neutrons produced in this fission reaction
n
9038
14254
10
23592
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UCLES 2005
E
00 A
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(ii) Data for binding energies per nucleon are given in Fig. 7.2.
Fig. 7.2
Calculate
1. the energy, in MeV, released in this fission reaction,
2. the mass equivalent of this energy.
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UCLES 2005
isotope binding energy per nucleon/ MeV
Uranium-235Xenon-142Strontium-90
7.598.378.72
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9702/04/O/N/06
9 Uranium-234 is radioactive and emits -particles at what appears to be a constant rate.
A sample of Uranium-234 of mass 2.65g is found to have an activity of 604 Bq.
(a) Calculate, for this sample of Uranium-234,
(i) the number of nuclei,
(ii) the decay constant, (iii) the half-life in years.
(iii) the half-life in years.
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UCLES 2006
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9702/04/O/N/06
(b) Suggest why the activity of the Uranium-234 appears to be constant.
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(c) Suggest why a measurement of the mass and the activity of a radioactive isotope is notan accurate means of determining its half-life if the half-life is approximately one hour.
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UCLES 2006
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9702/04/O/N/07
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UCLES 2007
10 (a) Explain what is meant by the binding energy of a nucleus.
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(b) Fig. 7.1 shows the variation with nucleon number (mass number) A of the binding energy per nucleon EB of nuclei.
0
BE
0 A
Fig. 7.1
One particular fission reaction may be represented by the nuclear equation23592U +
10n
14156Ba +
9236Kr + 3
10n.
(i) On Fig. 7.1, label the approximate positions of
1. the uranium (23592U) nucleus with the symbol U, 2. the barium (14156Ba) nucleus with the symbol Ba, 3. the krypton ( 9236Kr) nucleus with the symbol Kr. [2]
(ii) The neutron that is absorbed by the uranium nucleus has very little kinetic energy. Explain why this fission reaction is energetically possible.
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(c) Barium-141 has a half-life of 18 minutes. The half-life of Krypton-92 is 3.0 s. In the fission reaction of a mass of Uranium-235, equal numbers of barium and krypton
nuclei are produced. Estimate the time taken after the fission of the sample of uranium for the ratio
number of Barium-141 nucleinumber of Krypton-92 nuclei
to be approximately equal to 8.
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tutorial 14 a2 a.pdf9702_s09_qp_4 16.pdf9702_s10_qp_41 14.pdf9702_s10_qp_41 15.pdf9702_s10_qp_42 15.pdf9702_w09_qp_41 16.pdf9702_w09_qp_42 18.pdf
9702_s05_qp_4 14.pdf9702_s05_qp_4 15.pdf9702_s07_qp_4 14.pdf9702_s07_qp_4 15.pdf9702_s08_qp_4 18.pdf9702_w05_qp_4 14.pdf9702_w05_qp_4 15.pdf9702_w06_qp_4 14.pdf9702_w06_qp_4 15.pdf9702_w07_qp_4 16.pdf9702_w07_qp_4 17.pdfUntitled