Atomic and Nuclear

Physics
Radioactivity
 Objectives:
 relate radioactivity to nuclear instability;
 discuss the spontaneous and random
nature of nuclear decay;
 identify the origins and environmental
hazards of background radiation
Radioactivity
 describe experiments to distinguish
between the three types of emissions from
radioactive substances;
 write and interpret equations for
radioactive decay;
 discuss the environmental hazards of
radioactive emissions;
Radioactivity
 discuss the necessary safety precautions
for handling and disposal of radioactive
material;
 explain ‘activity’, ‘decay constant’ and
‘half-life’, and use the relationship A = λN
 use the law of decay dN  N and N  N exp(t )
0
dt
 use the relation T  ln 2 to solve problems
1
2
Radioactivity
 describe an experiment to determine the
half-life of a radioactive isotope with a
short half-life
 discuss uses of radioisotopes as tracers
for carbon dating and in radiotherapy
 describe the operation of simple detectors.
 What do we mean by
Radioactivity?
Radioactive decay is the process in which an unstable atomic
nucleus loses energy by emitting radiation in the form of
particles or electromagnetic waves.

There are numerous types of radioactive decay. The general idea:

An unstable nucleus releases

energy to become more stable
 Early Pioneers in Radioactivity
Rutherford: Roentgen:
Discoverer Discoverer of
Alpha and X-rays 1895
Beta rays 1897

The Curies:
Becquerel:
Discoverers of
Discoverer of
Radium and
Radioactivity
Polonium 1900-
1896
1908
 Radioactivity

 In 1896, Henri Becquerel discovered, almost by accident, that

uranium can blacken a photographic plate, even in the dark.

 Uranium emits very energetic radiation ‑ it is radioactive.

Henri Becquerel (1852-1908)

In 1903, he shared the Nobel Prize in Physics Image of Becquerel's photographic plate
with Pierre and Marie Curie "in recognition of the which has been fogged by exposure to
extraordinary services he has rendered by his radiation from a uranium salt.
discovery of spontaneous radioactivity".
Radioactivity

 Then Marie and Pierre Curie

discovered more radioactive
elements including polonium and
radium.

 Scientists soon realised that there

were three different types of Marie Curie (1867-1934)
radiation.

 These were called alpha (α), beta

(β), and gamma (γ) rays from the
first three letters of the Greek
alphabet.

Pierre Curie (1859-1906)

Three Common Types of
Radioactive Emissions
Alpha

Beta

Gamma
 Alpha, Beta and Gamma Radiation in a magnetic field

The diagram shows how the different types are affected by a

magnetic field.
 The alpha beam is a flow of
positively (+) charged
particles, so it is equivalent
to an electric current.

 It is deflected in a direction
given by Fleming's left‑hand
rule ‑ the rule used for
working out the direction of
the force on a
current‑carrying wire in a
magnetic field.
Alpha, Beta and Gamma Radiation in a magnetic field

 The beta particles are much lighter than the alpha particles
and have a negative (‑) charge, so they are deflected more,
and in the opposite direction.

 Being uncharged, the

gamma rays are not
deflected by the field.
 Alpha and beta particles are
also affected by an electric
field ‑ in other words, there
is a force on them if they
pass between oppositely
charged plates.
Deflection by electric fields
- - - Alpha and beta particles are
deflected in opposite
directions due to their
opposite charges.
Due to their much larger
mass alpha particles are
deflected far less than beta.
Gamma rays are not
+ + +
deflected because they are
Electric field produced by not charged.
positively and negatively
charged plates
Ionising Properties
 α ‑particles, β ‑particles and γ ‑ray photons are all very
energetic particles.

 We often measure their energy in electron‑volts (eV)

rather than joules.

 Typically the kinetic energy of an α ‑particle is about 6

million eV (6 MeV).

 We know that radiation ionises molecules by `knocking'

electrons off them.

 As it does so, energy is transferred from the radiation to

the material.

 The next diagrams show what happens to an α‑particle

Ionising Properties
Penetrating power of alpha radiation.

 Since the α-particle is a heavy, relatively

slow‑moving particle with a charge of +2e, it
interacts strongly with matter.

 It produces about 1 x 105 ion pairs per cm of its

path in air.

 After passing through just a few cm of air it has

lost its energy.
Penetrating power of beta radiation.

 The β‑particle is a much lighter particle than

the α ‑particle and it travels much faster.

 Since it spends just a short time in the vicinity

of each air molecule and has a charge of only
‑le, it causes less intense ionisation than the α
‑particle.

 The β ‑particle produces about 1 x 103 ion pairs

per cm in air, and so it travels about 1 m before
it is absorbed.
Penetrating power of gamma radiation.

 A γ‑ray photon interacts weakly with matter

because it is uncharged and therefore it is
difficult to stop.

 A γ ‑ray photon often loses all its energy in one

event.

 However, the chance of such an event is small

and on average a γ ‑photon travels a long way
before it is absorbed.
Alpha, Beta and Gamma Radiation
The penetrating power of
alpha, beta and gamma radiation

Paper or a few 1cm of Several cm of lead or

cm of air stops aluminium or 1m 1m of concrete is
alpha particles of air stops beta needed to stop
particles gamma rays
Properties of Alpha, Beta and Gamma Radiation: summary
Detection of radiation.

Geiger‑Muller (GM) tube

 This can be used to detect alpha, beta, and gamma
radiation.
 Geiger-Muller (GM) tube

 The `window' at the end is thin enough for alpha particles to

pass through.
 If an alpha particle enters the tube, it ionizes the gas inside.
 This sets off a high‑voltage spark across the gas and a
pulse of current in the circuit.
 A beta particle or burst of gamma radiation has the same
effect.
 Ionisation Chamber

 The ionisation chamber is another detector which uses the

ionising power of radiation.
 The chamber contains fixed electrodes, which attract
electrons and ions produced by the passage through the
chamber of high‑speed particles or rays.
 When the electrodes
detect ions or
electrons, a circuit is
activated and a pulse
is sent to a recording
device.
 Does not distinguish
between types of
radiation
Cloud and Bubble Chamber
 Have you looked at the sky and seen a cloud trail behind a high
flying aircraft?
 Water vapour in the air condenses on the ionised exhaust gases
from the engine to form droplets that reveal the path of the plane.
 A cloud chamber produces a similar effect using alcohol vapour.
 Radiation from a radioactive source ionises the cold air inside the
chamber.
 Alcohol condenses on the ions of air to form a trail of tiny white
droplets along the path of the radiation.
 The diagrams below show some typical tracks
Cloud and Bubble Chamber
 The α‑radiation produces dense straight tracks
showing intense ionisation.

 Notice that all the tracks are similar in length.

 The high‑energy β‑ray tracks are thinner and less

intense.

 The tracks vary in length and most of the tracks

are much longer than the α ‑particle tracks.

 The γ‑rays do not produce continuous tracks.

 A bubble chamber also shows the tracks of

ionising radiation. The radiation leaves a trail of
vapour bubbles in a liquid (often liquid hydrogen).
Stability

 If you plot the neutron number

N against the proton number Z
for all the known nuclides, you
get the diagram shown here
 Can you see that the stable
nuclides of the lighter elements
have approximately equal
numbers of protons and
neutrons?
 However, as Z increases the
`stability line' curves upwards.
 Heavier nuclei need more and
more neutrons to be stable.
A plot of neutron number versus proton
Can we explain why? number is also called Segre plot.
Stability

 It is the strong nuclear force that holds the nucleons

together, but this is a very short range force.

 The repulsive electric force between the protons is a longer

range force.

 So in a large nucleus all the protons repel each other, but

each nucleon attracts only its nearest neighbours.

 More neutrons are needed to hold the nucleus together

(although adding too many neutrons can also cause
instability).

 There is an upper limit to the size of a stable nucleus,

because all the nuclides with Z > 83 are unstable.
Radioactive decay
equations
Where do these particles come
from ?

 These particles generally come

from the nuclei of atomic isotopes
which are not stable.

 The decay chain of Uranium

produces all three of these forms
of radiation.

 Let’s look at them in more detail…

Note: This is the

Alpha Particles (a)

atomic weight, which
is the number of
protons plus neutrons

Radium Radon
+ n p
p n
R226 Rn222
a (4He)
88 protons 86 protons 2 protons
138 neutrons 136 neutrons 2 neutrons

The alpha-particle (a) is a Helium nucleus.

It’s the same as the element Helium, with the

electrons stripped off !
Alpha decay
Alpha particles consist of two protons plus two
neutrons.
They are emitted by some of the isotopes of the
heaviest elements.
Example: The decay of Uranium 238

238 234 4
U Th + α
92 90 2
Uranium 238 decays to Thorium 234 plus an alpha particle.

Notes:
1. The mass and atomic numbers must balance on each side
of the equation: (238 = 234 + 4 AND 92 = 90 +2)
2. The alpha particle can also be notated as: 4
He
2
Question
Show the equation for Plutonium 239 (Pu)
decaying by alpha emission to Uranium (atomic
number 92).

239 235 4

94
Pu U + 2
α
92
Alpha decay
4
 An alpha‑particle is a helium nucleus and is written 2 He or 24
 It consists of 2 protons and 2 neutrons.
 When an unstable nucleus decays by emitting an α ‑particle
 it loses 4 nucleons and so its nucleon number decreases
by 4.
 Also, since it loses 2 protons, its proton number decreases
by 2
 The nuclear equation is

A A 4 4
Z X Z 2 Y  2

Note that the top numbers balance on each side of the

equation. So do the bottom numbers.
 Beta Particles (b)
Carbon Nitrogen +
C14 e-
N14

6 protons 7 protons electron

8 neutrons 7 neutrons (beta-particle)

We see that one of the neutrons from the C14 nucleus

“converted” into a proton, and an electron was ejected.
The remaining nucleus contains 7p and 7n, which is a nitrogen
nucleus. In symbolic notation, the following process occurred:

np+e (+n)
Yes, the same
neutrino we saw
previously
Beta decay
Beta particles consist of
high speed electrons.
They are emitted by
isotopes that have too many
neutrons.
One of these neutrons
decays into a proton and an
electron. The proton
remains in the nucleus but
the electron is emitted as
the beta particle.
Example: The decay of Carbon 14

14 14 0
C N + -
6 7 -1 β
Carbon 14 decays to Nitrogen 14 plus a beta particle.

Notes:
1. The beta particle, being negatively charged, has an
effective atomic number of minus one.
2. The beta particle can also be notated as: 0
e
-1
Question
Show the equation for Sodium 25 (Na), atomic
number 11, decaying by beta emission to
Magnesium (Mg).

25 25 0
Na
12
Mg + -1 β
-
11
 Beta decay

 Many radioactive nuclides decay by β‑emission.

 This is the emission of an electron from the nucleus.
 But there are no electrons in the nucleus!
 What happens is that one of the neutrons changes into a
proton (which stays in the nucleus) and an electron (which is
emitted as a β‑particle).
 This means that the proton number increases by 1, while
the total nucleon number remains the same.
 The nuclear equation is

A A 0
Z X Y e
Z 1 1

Notice again, the top numbers balance, as do the bottom ones.

 Beta decay

 A radio‑nuclide above the

stability line decays by
β‑emission.
 Because it loses a neutron
and gains a proton, it moves
diagonally towards the
stability line, as shown on
this graph.

Gamma decay
 Gamma‑emission does not change the structure of the
nucleus, but it does make the nucleus more stable because
it reduces the energy of the nucleus.
Gamma decay
Gamma decay is the emission of electromagnetic radiation
from an unstable nucleus
Gamma radiation often occurs after a nucleus has emitted
an alpha or beta particle.

Example: Cobalt 60

60 60 0
Co Co + γ
27 27 0
Cobalt 60 with excess ENERGY decays to
Cobalt 60 with less ENERGY plus gamma radiation.
 Gamma particles (g)
In much the same way that electrons in atoms can be in an
excited state, so can a nucleus.

Neon Neon
Ne20 Ne20 +

10 protons 10 protons
gamma
10 neutrons 10 neutrons
(in excited state) (lowest energy state)

A gamma is a high energy light particle.

It is NOT visible by your naked eye because it is not in

the visible part of the EM spectrum.
Gamma Rays

Neon
Ne20

Neon
Ne20 +

The gamma from nuclear decay

is in the X-ray/ Gamma ray
part of the EM spectrum
(very energetic!)
How do these particles differ ?
Mass*
Particle Charge
(MeV/c2)

Gamma (g) 0 0

Beta (b) ~0.5 -1

Alpha (a) ~3752 +2

* m = E / c2
Write equations showing how Lead 202 could
decay into Gold. (This cannot happen in reality!)
Element Sym Z 202 198 4
Pb Hg + α
Platinum Pt 78 82 80 2
Gold Au 79
198 194 4
Mercury Hg 80 Hg Pt + α
80 78 2
Thallium Tl 81
Lead Pb 82 194 194 0
-
Pt Au + β
Bismuth Bi 83 78 79 -1

There are other correct solutions

 Decay chains

 A radio‑nuclide often produces an unstable daughter

nuclide.
 The daughter will also decay, and the process will continue
until finally a stable nuclide is formed.
 This is called a decay chain or a decay series.
 Part of one decay chain is shown below
Decay chains

 When determining the

products of decay series,
the same rules apply as in
determining the products of
alpha and beta, or artificial
transmutation.

 The only difference is

several steps are involved
instead of just one.
Half-life
 Suppose you have a sample of 100 identical nuclei.
 All the nuclei are equally likely to decay, but you can never
predict which individual nucleus will be the next to decay.
 The decay process is completely random.
 Also, there is nothing you can do to `persuade' one nucleus
to decay at a certain time.
 The decay process is spontaneous.
 Does this mean that we can never know the rate of decay?
 No, because for any particular radio‑nuclide there is a
certain probability that an individual nucleus will decay.
 This means that if we start with a large number of identical
nuclei we can predict how many will decay in a certain time
interval. (process obeys statistical law of chance)
Half-Life
dN
 N
dt
N dN t
N0 N   o dt

ln N N
N0  t
 t
N  N 0e
λ is the radioactivity decay constant
Half life
 The radioactivity decay constant can be
interpreted as:
 The fraction per second of the decaying
atoms
 The probability of an atom decaying in the
next second
Half-life

PThe

 rate
AEof activity A, is proportional to
the number of disintegrating atoms
6
P  30  10A  Bq
A e  2.5MeV 0
 t

 Power = AE 7 1
P  7.5 10 MeVs
Example: For a source that has an activity of 30MBq and emits particles
Of energy 2.5 MeV, the energy transfer per second is

5 1
P  1.2  10 Js
Half-life
 The Half-life is the time for the mass of a
radioactive isotope to disintegrate to half
its initial mass
1 0.693
T1  ln 2 
2  
Half life (Example)
20
NA
 0  1.2  10of
sample a radioactive isotope initially
contains
  3.6 10 s 1.2
 3 x11020 atoms of the isotope.

The decay constant for the isotope is 3.6 x

t 101000
-3
s-1s Calculate:
 The number3 of 1 atoms of the isotope remaining
t  3.6 10 s 1000s  3.6
after 1000s
 t 20  3.6 18
N The
N 0 eactivity
 1of.2the
10 e after
sample  31000s
.2 10
3 18 16
A  N  3.6 10  3.2 10  1.2 10 Bq
Another Contribution from Rutherford:
Half-life of Radioactive Atoms
The half-life of a radioactive substance, is the time required
for one half of it to decay.
Half-life

 Iodine‑131 is a radioactive isotope of iodine.

 The chart illustrates the decay of a sample of iodine‑131.
 On average, 1 nucleus disintegrates every second for every
1000 000 nuclei present.
To begin with, there are 40 million undecayed nuclei.
8 days later, half of these have disintegrated.
With the number of undecayed nuclei now halved, the number of
disintegrations over the next 8 days is also halved.
It halves again over the next 8 days... and so on.
Iodine‑131 has a half‑life of 8 days.
Half-life
 The half‑life of a radioactive isotope is the time
taken for half the nuclei present in any given
sample to decay.
 Activity and Half-life
 In a radioactive sample, the average number of disintegrations
per second is called the activity.
 The SI unit of activity is the becquerel (Bq).
 An activity of, say, 100 Bq means that 100 nuclei are
disintegrating per second.
 The graph shows how,
on average, the
activity of a sample of
iodine‑131 varies with
time.
 As the activity is
always proportional to
the number of
undecayed nuclei, it
too halves every 8
days.
 Activity and Half-life
 So `half‑life' has another meaning as well:
The half‑life of a radioactive isotope is the time taken for the
activity of any given sample to fall to half its original value.
 Exponential Decay

 Any quantity that reduces by the same fraction in the same

period of time is called an exponential decay curve.
 The half life can be calculated from decay curves
 Take several values and then take an average
Lifetime (t)
 The “lifetime” of a particle is an alternate definition of
the rate of decay, one which we prefer.

 It is just another way of expressing how fast the substance

decays..

 It is simply: 1.44 x h, and one often associates the

letter “t” to it.

 The lifetime of a “free” neutron is 14.7 minutes

{t (neutron)=14.7 min.}

 Let’s use this a bit to become comfortable with it…

Lifetime (I)
 The lifetime of a free neutron is 14.7 minutes.

 If I had 1000 free neutrons in a box, after 14.7

minutes some number of them will have decayed.

 The number remaining after some time is given by the

radioactive decay law

N0 = starting number of
 t /
N  N 0e particles
t = particle’s lifetime

This is the “exponential”. It’s

value is 2.718, and is a very useful
number. Can you find it on your
calculator?
 Lifetime (II)
 t /
Note by slight rearrangement of this formula: N  N 0e
Fraction of particles which did not decay: N / N0 = e-t/t
1.20
# Time Fraction of
lifetimes (min) remaining 1.00

neutrons

Fraction Survived
0.80

0t 0 1.0 0.60

1t 14.7 0.368 0.40

2t 29.4 0.135 0.20

3t 44.1 0.050 0.00

0 2 4 6 8 10

4t 58.8 0.018 Lifetimes

5t 73.5 0.007 After 4-5 lifetimes, almost all of the

unstable particles have decayed away!
Lifetime (III)
 Not all particles have the same lifetime.

 Uranium-238 has a lifetime of about 6 billion

(6x109) years !

 Some subatomic particles have lifetimes that are

less than 1x10-12 sec !

 Given a batch of unstable particles, we cannot

say which one will decay.

 The process of decay is statistical. That is, we can

only talk about either,
1) the lifetime of a radioactive substance*, or
2) the “probability” that a given particle will decay.
Lifetime (IV)
 Given a batch of 1 species of particles, some will decay
within 1 lifetime (1t), some within 2t, some within 3t, and
so on…

 We CANNOT say “Particle 44 will decay at t =22 min”.

You just can’t !

 All we can say is that:

 After 1 lifetime, there will be (37%) remaining
 After 2 lifetimes, there will be (14%) remaining
 After 3 lifetimes, there will be (5%) remaining
 After 4 lifetimes, there will be (2%) remaining, etc
Lifetime (V)

 If the particle’s lifetime is very short, the particles decay away

very quickly.

 When we get to subatomic particles, the lifetimes

are typically only a small fraction of a second!

 If the lifetime is long (like 238

U) it will hang around for a very long
time!
 Lifetime (IV)
What if we only have 1 particle before us? What can we say
about it?

Survival Probability = N / N0 = e-t/t

Decay Probability = 1.0 – (Survival Probability)

# lifetimes Survival Probability Decay Probability =

1.0 – Survival Probability
(percent) (Percent)
1 37% 63%
2 14% 86%
3 5% 95%
4 2% 98%
5 0.7% 99.3%
Summary
 Certain particles are radioactive and undergo decay.

 Radiation in nuclear decay consists of a, b, and g particles

 The rate of decay is give by the radioactive decay law:

Survival Probability = (N/N0)e-t/t

 After 5 lifetimes more than 99% of the initial particles

have decayed away.

 Some elements have lifetimes ~billions of years.

 Subatomic particles usually have lifetimes which are

fractions of a second!
Online Simulations
Build an atom - PhET - Build an atom out of protons, neutrons, and
electrons, and see how the element, charge, and mass change.
Then play a game to test your ideas!
Atom builder - Freezeway.com
Build an atom - eChalk
Types of Radiation - S-Cool section on types of radiations including an
animation of absorption and a couple of decay equations to fill in on
screen.
Decay series - Fendt
BBC AQA GCSE Bitesize Revision:
Atoms, isotopes & radioactivity - Core Science
Structure of an atom
Isotopes
Alpha, beta & gamma radiation
Penetration properties
Deflection radiation
Radioactive decay equations