Lesson 10 • Isotopes • Radioactivity

– Discovery of Radioactivity – Theory of Radioactivity – Types of Radiations – Properties of Alpha (α ) Rays – Properties of gamma (γ) rays – Properties of beta (β) particles – Geiger-Müller tube – Cloud Chamber – Radioactive Decay – Half-Life

• Energy Levels

• Nucleons – particles found in the nucleus of an atom – neutrons

– protons

• Atomic Number (Z) – number of protons in the nucleus

• Mass Number (A) – sum of the number of protons and neutrons

• Isotopes – atoms with identical atomic numbers but different mass numbers

• Nuclide – each unique atom

A Review of Atomic Terms

Isotopes

Isotopes • Main Sub-atomic Particles

a For stable nuclides, the isotopic abundance is given; this is the fraction of atoms of this type found in a typical sample of the element. For radioactive nuclides, the half-life is given. b Following standard practice, the reported mass is that of the neutral atom, not that of the bare nucleus.

c Spin angular momentum in units of ћ.

Isotopes What’s an isotope?

Two or more varieties of an element having the same number of protons but different number of neutrons. Certain isotopes are “unstable” and decay to lighter isotopes or elements. Deuterium and tritium are isotopes of hydrogen. In addition to the 1 proton, they have 1 and 2 additional neutrons in the nucleus respectively*.

Another prime example is Uranium 238, or just 238U.

Radioactivity

• Radioactivity – the spontaneous decomposition of a nucleus forming a different nucleus and producing one or more additional particles

• Nuclear Equation – shows the radioactive decomposition of an element

146C → 14

7N + 0-1e

• Nuclear Forces – strong nuclear force holds neutrons and protons together to form a nucleus (counters electromagnetic repulsion). Weak nuclear force operates within individual nucleons and gives rise to some kinds of radioactivity

Discovery of Radioactivity

• Antoine Henri Becquerel (1852-1908) Henri Becquerel in 1896 discovered that uranium

compounds emitted invisible radiation, which could: blacken a photographic plate ionize a gas

Noticed the fogging of photographic plate by uranium crystals

• Pierre Curie (1859-1906), Marie Curie (1867-1934) Further studies of uranium and discovery of polonium and

radium. Marie received two Nobel prizes. She died from the effects of radiation doses received during her experiments

• Ernest Rutherford (1871-1937) His understanding of atomic structure helped us

understand the role of the nucleus.

Theory of Radioactivity

• Some Terminology • A neutral atom has equal numbers of protons in its nucleus and

electrons in orbit about the nucleus. • An atom can gain or lose electrons, becoming a negative or positive ion • The proton number (or atomic number) Z of an element is the number

of protons in each nucleus of the atoms of the element. All its nuclei have the same proton number

• The nucleon number (or mass number) A of an atom is the number of nucleons (protons plus neutrons) in its nucleus

• A given element can have several values of A, since the number of neutrons can vary. Atoms of an element with equal numbers of neutrons constitute an isotope of that element

• A nuclide refers to the nucleus of an atom, characterized by its A and Z value, or to an atom to which such a nucleus belongs

Theory of Radioactivity

Hydrogen has 3 isotopes:

Note: Chemical reactions only involve the outer electrons of atoms, so isotopes of a given element act the same chemically. For example, the most common form of water is made up of molecules of H2O. But there also exist water molecules, about 1 part in 5000, in the form of D2O (‘heavy water’).

Theory of Radioactivity • Ionization occurs when neutral atoms have electrons knocked off them, producing

positive ions and free electrons. • Radioactivity is simply the spontaneous disintegration of nuclei to move from

an unstable state to a stable one. • There are three types of radiation emitted in radioactive decay: alpha particles,

beta particles and gamma rays. • Alpha Particles(α) • These are helium nuclei, and therefore consist of two protons and two

neutrons. • Beta Particles (β- β+) • There are two types of beta particle: beta-plus and beta-minus. The beta-plus

is sometimes called an anti-electron. Each can travel up to 98% the speed of light. A beta-minus particle is released as a result of a neutron changing into a proton, while a beta-plus particle is released as a result of a proton changing into a neutron.

• Gamma Rays (γ) • Gamma rays are high energy, short wavelength photons of electromagnetic

radiation. Gamma rays are emitted because the atom is usually in a high energy state after emission of alpha or beta particles. This unstable state is made stable by emission of gamma ray photons.

Theory of Radioactivity

• A strip of polythene or a strip of Perspex rubbed with wool become charged by friction, negatively and positively respectively. If one of them is held close to the cap of the electroscope, and the cap is momentarily touched with a finger, the cap acquires a charge opposite to that of the charged strip.

• When the strip is removed, the charge spreads itself around the cap, the rod and the gold leaf.

• The leaf is seen to diverge, since it and the metal rod have the same charge.

Theory of Radioactivity • When a radium source (held in tongs, and well away from

the face) is held close to the cap, without touching it, the leaf is seen to collapse. This is due to the ionization of the air produced by the radiation emitted by the radium, which produces positive ions and negative electrons. If the cap is negative it attracts the ions, and if it is positive it attracts the electrons. In either case the electroscope is neutralized.

The Electroscope

Types of Radiation

• They can be separated by a magnetic field, since those that are charged will be deviated:

• A dark spot is produced on the photographic plate, where impacted by radiation.

Types of Radiation • From the directions of the deflections produced by the magnetic field

(using Fleming's left hand rule - covered in other notes) we can infer that:

• The gamma rays are uncharged, since they are undeviated. They are now known to be electromagnetic radiation of the shortest known wavelength

• The alpha particles are positively charged. They are now known to be helium nuclei

• The beta particles are negatively charged. They are now known to be electrons

• Note: The above diagram is something of a ‘composite’ - it indicates the relative directions of the deflections but not the true relative sizes of deflections. Since alpha particles are helium nuclei, they are 1000s of times more massive than beta particles (electrons) - if the magnetic field were strong enough to move the alphas by the amount indicated, the betas would be deviated so much as to not reach the plate.

Properties of Alpha (α ) Rays

• An alpha particle is an helium nucleus ( ) • The alpha particles short out of radioactive substances have

velocities ranging from (1.4-1.7)x107m/s • They produce high ionisation in the gas through which they

pass. (α ) particles have 100 times than beta (β) and about 10,000times that of gamma (γ) rays.

• They feebly affect photographic paper • They are scattered by nuclei of heavy elements such as gold

and produce heat due to the stoppage of (α ), (β) and (γ) by the radioactive substance.

• Radium-226 (‘Ra-226’) is an alpha source.

He4

2

Properties of gamma (γ) rays

• They are E-M waves of short wavelengths (0.005Å to 0.5Å). They are not charged, hence not affected by either electric or magnetic field and travel with the speed of light.

• They produce fluorescence and affect photographic plate. • They ionise the gas through which they pass but the

ionisation is small • They are more penetrating than even beta particles and

can pass though an iron plate of about 30 cm thickness. Several cm of lead or several metres of concrete are required to absorb them significantly. Cobalt-60 (‘Co-60’) is a gamma source.

• They are diffracted by crystals just like X rays are.

Properties of beta (β) particles

• The beta particles possess –ve charge and mass equal to that of an electron. They are identical to electrons

• All (β) emitted from a substance do not have the same velocity. They range from 0.3c to 0.99c. At high velocities, e/m is found to decrease , indicating an increase in mass according to the equation

• The ionising power is low hence the range is large • They affect photographic plate and produce fluorescence in certain

compounds e.g. barium platino cyanide • They are deflected by electric and magnetic fields, their direction

indicating that they are negatively charged particles. • They penetrate through thin foils and their penetration power is

greater than that of alpha rays. • Strontium-90 (‘Sr-90’) is a beta source.

2

2

0

1c

v

mm

Geiger-Müller tube (‘GM tube’) • The Figure shows the experimental arrangement of Geiger and

Marsden. • Their alpha source was a thin-walled glass tube of radon gas. The

experiment involves counting the number of alpha particles that are deflected through various scattering angles φ.

The dots are alpha-particle scattering data for a gold foil, obtained by Geiger and Marsden. The solid curve is the theoretical prediction, based on the assumption that the atom has a small, massive, positively charged nucleus. The data have been adjusted to fit the theoretical curve at the experimental point that is enclosed in a circle.

Geiger-Müller tube (‘GM tube’)

A Geiger-Müller tube (‘GM tube’) - a pulse of current is produced when it detects radiation. It can be connected to a scaler or a ratemeter. A scaler counts the number of pulses. A ratemeter gives the average number of pulses per second or per minute, and may give a click for each pulse (a ‘Geiger counter’).

Cloud Chamber or Bubble Chamber

• Though we cannot see radiation directly, we can see where it has been using these devices. A cloud chamber contains vapour and as an alpha particle, for example, passes though, it collides with atoms, producing a path of ions. Vapour condenses along the path of ions, making it visible. A bubble chamber contains liquid, and vapour bubbles are formed along the ion path, again making it visible.

• Alpha particles are strongly ionizing and lose their energy quickly, and being relatively massive, they are not easily deflected by impacts - so they produce short, thick, straight paths

• Beta particles are less strongly ionizing, and being light are easily deflected - so they produce long, thin, irregular paths

• Gamma rays can eject electrons from atoms, and these produce the paths seen

Radioactive Decay

• Alpha-Particle Production Alpha particle – helium nucleus

– Examples

Types of Radioactive Decay

• Net effect is loss of 4 in mass number and loss of 2 in atomic

number.

Radioactive Decay

• Beta-Particle Production

• Net effect is to change a neutron to a proton.

Beta particle – electron

– Examples

Radioactive Decay

• Gamma Ray Release

• Net effect is no change in mass number or atomic

number.

• Gamma ray – high energy photon

– Examples

Radioactive Decay

• Positron production

• Net effect is to change a proton to a neutron.

• Positron – particle with same mass as an electron but with a positive charge

(antimatter version of an electron)

– Examples

Radioactive Decay

• Electron capture • Inner orbital electron is captured. New nucleus formed.

Neutrino and gamma ray produced

• Net effect is to change a proton to a neutron

20180Hg + 0-1e → 20179Au + ν + 00γ

Law of radioactive disintegration Let N be the number of atoms present in a particular radioactive element at a given time t.

then the rate of decrease (decay) dt

dN is proportional to N (the number of un decayed

particles) or dt

dNN

N

dt

dN, or A= N

Where λ is a constant known as the disintegration constant of the respective element. It is

defined as the ration of the amount of the substance which disintegrates in unit time to the

amount of substance present

)1(

,

ln,ln,

,

0

0

0

0

0

0

0

t

t

tN

N

tN

N

eNN

eN

N

tN

Ntdt

N

dN

dtN

dNN

dt

dN

This equation shows that the number of atoms of a given radioactive substance decreases

exponentially with time.

Half-Life • The “half-life” (h) is the time it takes for half the atoms of a radioactive substance to

decay. • For example, suppose we had 20,000 atoms of a radioactive substance. If the half-life is 1 hour, how many atoms of that substance would be left after:

10,000 (50%)

5,000 (25%)

2,500 (12.5%)

1 hour (one lifetime) ?

2 hours (two lifetimes) ?

3 hours (three lifetimes) ?

Time #atoms

remaining % of atoms remaining

Half-Life As nuclei in a radioactive sample decay, the activity gets less, till eventually there are no more

nuclei left to decay.

The half-life of a radioactive source is the time for the activity to fall by half

Or, since the activity of a source is directly proportional to the number of undecayed nuclei, then:

The half-life of a radioactive source is the time for half the undecayed nuclei to decay

Half-Life From equation (1) above if

2

1T is the half life period, the time required for half of the

radioactive substance to disintegrate from 2

0

ONtoN then

)2(693.02ln

2

2ln

,2ln1ln

,2

1,

2

1

2

2

220

0

1

1

11

T

e

eeNN

T

T

TT

Substitute equation (2) in (1), then we have

2

1

2

1

)5.0(

5.0,

0

2ln2

1(2ln

2ln

0

T

t

T

t

T

t

N

N

bygivenisttimesomeafterremainingfractiontheso

ebuteeN

N

λ (lambda) is a positive constant called the decay constant. It has the unit s-1

, hr-1

, day-1

or yr-1

The minus sign is included in A= N because N decreases as the time t in seconds (s)

increases.

Half-Life

The decay constant λ of a radioactive nuclide is the probability that an individual nucleus will

decay within a unit time.

The value of λ is constant for any particular nuclide and zero for a stable nuclide.

Nuclear Fission

Nuclear fission

Means splitting up

A large nucleus (A 200) splits into two. The daughter fragments have higher binding energy

than the parent. They are more stable.

It was found (in 1939) that if uranium was bombarded with neutrons (these have no charge and

are not repelled by the nuclei), that a uranium nucleus could be split into two nuclei. This is

nuclear fission (it is not the same as spontaneous radioactivity).

One such splitting is:

e. g EnergynKrBanU 1

0

92

36

141

56

236

92

1

0

235

92 3

Nuclear Fusion

Nuclear fusion

Means joining together. Nuclear fusion: two (or more) atomic nuclei form a single heavier

nucleus. The reaction only takes place at very high densities and temperatures.

There are many examples of fusion reactions. The fusion of deuterium with tritium to make

helium (plus a neutron) is one of the more common ones -. Termed the D-T reaction.

nHeHH 1

0

4

2

3

1

2

1

Other examples incude:

energyHHeHeHe

andenergyHHHenergyHHH

1

1

4

2

3

2

3

2

0

0

3

2

1

1

2

1

0

0

0

1

2

1

1

1

1

1

2

,,

The fusion reaction of two (or more) nuclei with masses lower than iron is exothermic (heat

given out).

Conversely, the fusion reaction of two (or more) nuclei with masses greater than iron is

endothermic (heat absorbed).

Applications of Radioactivity

i. Many satellites use radioactive decay from isotopes with long half-lives for power because energy can be produced for a long time without refueling.

ii. Isotopes with a short half-life give off lots of energy in a short time and are useful in medical imaging, but can be extremely dangerous.

iii. The isotope carbon-14 is used by archeologists to determine age.

Applications of Radioactivity

iv. Sterilizing • Gamma rays can kill bacteria, which makes them useful for sterilizing

medical instruments after they have been sealed. A disposable syringe, for example, would be sealed in a plastic container and the container then exposed to gamma rays, killing the bacteria inside.

v. Controlling thickness • The amount of beta particles absorbed by the paper depends on its

thickness. The gap between the rollers can be automatically adjusted, keeping the beta count rate, and therefore the thickness of the paper, constant.

• Alpha particles are not used since they are completely absorbed by even thin paper. Gamma rays are not used because they would not be absorbed at all by the paper.

• A similar process to the above can be used to automatically control the thickness of steel sheet, but in this case a gamma source would be used.

Applications of Radioactivity

vi. Nuclear-Energy Power Plants

Harmful Radiation

• Radiation becomes harmful when it has enough energy to remove electrons from atoms.

• The process of removing an electron from an atom is called ionization.

• Visible light is an example of nonionizing radiation.

• UV light is an example of

ionizing radiation.

Harmful Radiation

• Ionizing radiation absorbed by people is measured in a unit called the rem.

• The total amount of radiation received by a person is called a dose, just like a dose of medicine.

• It is wise to limit your exposure to ionizing radiation whenever possible.

• Use shielding materials, such as lead, and do your work efficiently and quickly.

• Distance also reduces exposure.

Sources of Radiation

• Ionizing radiation is a natural part of our environment.

• There are two chief sources of radiation you will probably be exposed to:

– background radiation.

– radiation from medical procedures such as x-rays.

• Background radiation results in an average dose of 0.3 rem per year for someone living in the United States.

Background Radiation

• Background radiation levels can vary widely from place

to place. – Cosmic rays are high energy

particles that come from outside our solar system.

– Radioactive material from nuclear weapons is called fallout.

– Radioactive radon gas is present in basements and the atmosphere.

Energy Levels

• In an atom, electrons around a central nucleus can only have particular energy values. These discrete values are termed 'energy levels'. In a diagram they are represented by horizontal lines, with the lowest level (the ground state) at the bottom and the highest level (ionisation) at the top.

Energy Levels

The following is an energy level diagram for hydrogen:

The ionisation energy of an atom is the minimum energy needed to completely remove an

electron from the atom in its ground state. For hydrogen, the ionisation energy = 13.6eV =

21.8x10-19J

Energy Levels

1. Electrons occupy “stationary states”(they do not radiate)

2. These orbits are quantized

We can account for spectral lines if , angular momentum is nnh

mvrL2

Pr ,

n = 1,2,3,4,…….

Also rnnhhr

prsoh

P 2,2

,, or

The circumference is a number of de-Broglie wavelengths

3. Transition between states leads to absorption/emission of a photon with energy

21 EEhf

BOHR’S POSTULATES

Nuclear Models

Each model has its own merit. Realize the concept of these models and apply them to explain nuclear phenomena such as nuclear decay and nuclear reactions.

Liquid drop model: strong force hold nucleons together as liquid drop

of nucleons (Bohr). Rnucleus = 1.2 A1/3.

Gas model: nucleons move about as gas molecules but strong mutual

attractions holds them together (Fermi).

Shell model: nucleons behave as waves occupying certain energy states

worked out by quantum mechanical methods.

Each shell holds some magic number of nucleons.

Magic numbers: 2, 8, 20, 28, 50, 82, 126. Nuclei with magic number of protons or neutrons are very stable.

The shell model

Quantum mechanics treats nucleons in a nucleus as waves.

Each particle is represented by a wavefunction.

The wavefunctions are obtained by solving a differential equation.

Each wavefunction has a unique set of quantum numbers.

The energy of the state (function) depends on the quantum numbers.

Quantum numbers are: n = any integer, the principle q.n. l = 0, 1, 2, ..., n-1, the orbital quantum number s = 1/2 or -1/2 the spin q.n. J = vector sum of l and s

The wavefunction n,l is even or odd parity.

The Shell Model

Energy states of nuclei are labelled using J = j1 + j2 + j3 + j4 + ... plus parity,

J +

Some Excited States of the 7Li

Nuclide

½ + ___________ 6.54 MeV

7/2 + ___________ 4.64

½ – ___________ 0.478 3/2 – ___________ Ground State

Energy Level Diagram of Nucleons

n l j (2j+1) Shell Notation total 7 6 13/2+ 1i 14 ~126 6 0 ½– 3p 2 6 1 3/2– 3p 4 6 2 5/2– 2f 6 6 3 7/2– 2f 8 6 4 9/2– 1h 10 6 5 11/2– 1h 12 ~82 5 0 ½+ 3s 2 5 2 3/2+ 2d 4 5 3 5/2+ 2d 6 5 4 7/2+ 1g 8 5 4 9/2+ 1g 10 ~50 4 0 ½– 2p 2 4 1 3/2– 2p 4 4 2 5/2– 1f 6 4 3 7/2– 1f 8 ~28 3 0 ½+ 2s 2 ~20 3 1 3/2+ 1d 4 3 2 5/2+ 1d 6 2 0 ½– 1p 2 ~8 1 3/2– 1p 4 1 0 ½+ 1s 2 ~2