Lecture 6
Radioactivity
Contents
Properties of nuclei
The isotopes of an element have the same Z value but different N and A values.
Charge and mass of nuclei
The proton charge = e  1.6  10 19 C
The neutron charge = 0 C.
Nuclear masses can be measured with great precision with the help of the mass
spectrometer and the analysis of nuclear reactions.
Mass of proton = 1.007276 u, mass of neutron = 1.008665 u, mass of electron =
0.000549 u, where u is the unified mass unit equal to 1/12 of mass of 126 C isotope
(nucleus plus 6 electrons): u=1.660559x10-27 kg.
The proton is about 1836 times more massive than the electron, and the masses of the
proton and the neutron are almost equal. The proton and neutron each have a mass of
about 1u.
1 unified mass unit is equivalent to:
The rest energy:
E=mc2
1 unified mass unit is equivalent to:
E  mc 2  (1.660559  10 27 kg)(3  108 m / s) 2  931.5MeV
The rest energy of an electron is 0.511 MeV.
There are four types of radiation that can be emitted by a radioactive substance:
 alpha () decay, where the emitted particles are 4 He nuclei;
 beta () decay, in which the emitted particles are either electrons or positrons;
 gamma () decay, in which the emitted rays are high-energy photons;
 neutrons.
Alpha particles barely penetrate a sheet of paper.
Beta particles can penetrate a few millimetres of aluminium.
Gamma rays can penetrate several centimetres of lead.
Neutrons penetrate several feet of water or concrete and they
are trapped more readily by lighter elements (e.g. hydrogen in
water) than by heavier ones like the lead used to stop gamma
rays.
The decay law
If N is the number of radioactive nuclei present at some
instant, the rate of change of N is
dN
 N or N  N 0 e  t .
dt
1
Here  is the decay constant or disintegration constant, N0 represents the number of
radioactive nuclei at t=0;
The half-life, T1 / 2 .
ln 2 0.693
T1 / 2 

.


After one half-life, there are N0/2 radioactive nuclei remaining, after two half-lives, half of
these will have decayed and N0/4 radioactive nuclei will be left, after three half-lives, N0/8
will be left, and so on.
The absolute value of the decay rate
dN
R
is called activity. The SI unit of activity is called the becquerel (Bq):
dt
1 Bq = 1 decay/s.
The decay processes
Two conservation laws apply to all nuclear processes:
 the conservation of nucleons: the total of the mass numbers must be equal on each side
of the equation,
 the conservation of charge: the total of the proton numbers must be equal on each side
of the equation.

Alpha decay
(6)
X  ZA42Y  24 He
If a nucleus emits an alpha particle, it loses two protons and two neutrons. Therefore N
decreases by 2, Z decreases by 2 and A decreases by 4.
 Beta decay
A
A
1

Z X  Z 1Y  
A
Z
X  Z A1Y     
When a radioactive nucleus undergoes beta decay, the daughter nucleus has the same number
of nucleons as the parent nucleus but the charge number is changed by 1.
n  p    
 Gamma decay
A
*
A
Z X Z X  
The nucleus in an excited energy state undergoes a decay to a lower energy state by emitting
a photon (gamma rays). Such photons have very great energy (in the range of 1 MeV to
! GeV) relative to the energy of visible light (about 1 eV).
A
Z
Nuclear reactions
A target nucleus X is bombarded by a particle a, resulting in a nucleus Y and a particle b:
a  X Y  b
In more compact form:
X a, bY
In addition to energy and momentum, the total charge and total number of nucleons must be
conserved in any nuclear reaction. For example 19 F  p,  16O :
1
19
16
4
1 H  9 F  8 O  2 He
We see that the total number of nucleons before the reaction (1+19=20) is equal to the total
number after the reaction (16+4=20). Furthermore, the total charge (Z=10) is the same before
and after the reaction.
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Binding energy
The total mass of a nucleus is always less than the sum of the masses of its individual
nucleons. According to the Einstein mass-energy relationship, if the mass difference, m, is
multiplied by c2, we obtain the binding energy of the nucleus.
There are two important processes that result in energy release from the nucleus. In nuclear
fission, a nucleus splits into two or more fragments. In nuclear fusion, two or more nucleons
combine to form a heavier nucleus.
Biological half-life
1
1
1
 phys  biol .
eff
T1 / 2 T1 / 2
T1 / 2
As an example 131
53 I has a physical half-life of 8 days, but when present in the thyroid
gland it has an effective half-life of 7.5 days.
Types of nuclear radiation and their interaction with matter
 -radiation
Large kinetic energy of several MeV (velocities of several thousand km/s).
This energy is lost through ionization or excitation of the molecules and atoms of the
surrounding medium.
Linear ion density (specific ionization) = n/l,
where n is the number of ion pairs produced by a particle and l - the length of a track.
For -particles: 20 000 - 80 000 ion pairs/cm.
The linear ion density is smaller with high-energy particles, and increases with
decreasing energy.
 -radiation
Effective range extends from 10 cm to several m in air, but is only few mm in water and
living tissues.
Linear ion density of the -particle is approximately 1000 times smaller than that of the particle. The process of absorption of -particles is extremely complex: ionization, excitation
– but not only, also chemical, photochemical, biological etc. effects.
 -radiation
Interaction with matter:
The photoelectric effect (photoeffect) - a photon interacts with an electron of an atom.
By transferring all of its energy the photon is annihilated and electron escapes from the atom.
1
hf  A  mv 2 ,
2
where h signs Planck’s constant, f – frequency of light wave, mv2/2 denotes the kinetic
energy of the moving electron and A is the work of release necessary to raise the electron
from some inner level to the atomic surface. After leaving the atom, the electron induces
excitation and ionization until its excess energy is lost.
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The Compton effect
A photon interacts with an electron, but it transfers only part of its energy to the electron, and
continues moving with a smaller energy in a changed direction.
Pair production
An electron-positron pair is produced by an  or X-ray photon in the vicinity of an atomic
nucleus. The photon must be at least 1,02 MeV i.e. two rest energies of electron (0.51 MeV).
---------------------------------------------------------------The attenuation coefficient due to the photoeffect is proportional to the third power of
the atomic number of a material. The reason why soft tissues do not absorb X-rays very
strongly is that they consists mainly elements of low atomic numbers, whereas bones absorb
more strongly, since they also contain relatively large proportions of elements of higher
atomic numbers. Because of its large atomic number (82), lead is a very good absorbent of radiation. Depending upon the wavelength, the half-value thickness of air is several hundred
m, and that of the living organism several dm.
Measurement of nuclear radiations
 Measuring devices based on gas
ionization:
ionization chambers, proportional
counters, Geiger-Miiller counters
Ionization chambers are mainly used in individual
radiation protection as pocket dosimeters of the size and
shape of a fountain pen. These are charge electrometers,
which progressively become discharged in
response to the radiation.
 Detectors based on luminescence
Every charged particle striking the detector
produces a scintillation (light pulse). Light is
converted into an electric signal by a
photomultiplier.
 Photochemical measuring devices
photographic plates, other
substances
Persons who work with the radiation are
usually provided with film badges. Some crystals (e.g.
alkali halides), glasses (e.g. phosphate glasses
containing silver, glasses containing cobalt or lead,
organic solids (e.g. plexi, PVC) become coloured in
irradiation.
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