Nuclear Instability
Contents
Basic Radioactivity
 Inverse Square Law of Gamma Radiation
 Exponential Law of Decay
 Probing Matter

Basic Radioactivity
Radiation is the decay of an unstable parent nucleus to a more
stable daughter nucleus by emitting particles and/or energy
Transmutation is the process in which the unstable nucleus decays to form
another nucleus of a different atom. If this new nucleus is unstable, it will
decay again, and this is known as a decay chain.
The decay chain be very long or very short. Some elements decay over
thousands of years, some after microseconds.
Basic Radioactivity
Isotopes of different elements may be radioactive. These
radioactive versions are called radioisotopes.
There are three types of radiation:
Radiation
Description
Penetration
Ionisation
Effect of E or B
field
Alpha (a)
Helium nucleus
2p + 2n
Q=+2e
Few cm air
Thin paper
Intense, about 104
ion pairs per mm.
Slight deflection as
a positive charge
Beta (b)
High speed
electron
Q = -1 e
Few mm of
aluminium
Less intense than
a, about 102 ion
pairs per mm.
Strong deflection
in opposite
direction to a.
Gamma (g)
Very short
wavelength em
radiation
Several cm lead,
couple of m of
concrete
Weak interaction
about 1 ion pair
per mm.
No effect.
Inverse Square Law of Gamma Radiation
To measure the variation of gamma ray intensity with distance, the above
experiment is used.
If Count Rate against 1/Distance2 is
plotted, a straight line is achieved.
The origin of the line is below zero
distance because the gamma source
is deep within its housing.
It is found that the counts per second, intensity, decreases with the square of the
distance, meaning if the distance is doubled, the intensity reduces by four times.
Inverse Square Law of Gamma Radiation
The inverse square relationship is therefore:
Where: I – intensity I0 – intensity at the source k – constant x – the distance from the source
It is more common to calculate counts from two points, if l0 is unknown:
When combined and rearranged gives:
&
Background Radiation – must be measured and taken into account when
performing radiation experiments. It comes in the following forms:
· Cosmic rays
· Radioactive material in the bricks of the building.
· Small amounts from medical and industrial uses.
· People (contain Carbon-14 amongst other radioisotopes)
Exponential Law of Decay
Radioactive decay is entirely random and unpredictable.
Chemical reactions involve the outer shell of electrons, BUT
radioactive decay involves the nucleus of an atom.
The rate of decay of any nuclide at a given time is directly
proportional to the number of atoms left at that time:
(The d/dt gives the rate of change)
(The minus sign indicates that N
decreases as time increases)
Incorporating the radioactive decay constant, λ, into this
equation gives:
The radioactive decay constant is “the fraction of the total number of nuclei present
that decays per unit time, provided that the time interval is small”
Exponential Law of Decay
The units of λ is s-1 (per second), but often the Becquerel is used:
1 Bq = 1 count per second
Over long time periods, the equation becomes:
Where: N – no of nuclei N0 – original number of nuclei
e – exponential number λ - decay constant t – time(s)
This relationship is known
as exponential decay, and
the graph of this is shown
here
The rate of decay is the
activity, measured in
Becquerels, Bq
Exponential Law of Decay
Half-life Defined as “the time taken for the activity of a sample to decrease
to half of some initial value” So:
After 1 half life
Activity=50%
After 2 half lives
Activity=25%
After 3 half lives
Activity=12.5%
etc...
Half-life can be related to the decay constant:
By definition:and:Therefore:-
Half-life is useful for ascertaining methods of storing radioactive waste.
The decay equations are useful for radioactive dating, using radioisotopes
such as carbon-14, rubidium-87, and hydrogen-3
Probing Matter
Methods of probing matter:
• Rutherford scattering
(described in “Particles, Radiation & Quantum Phenomena”)
• Electron diffraction tube
Electrons can be shown to have simple wave properties by using an electron
diffraction tube as shown above. A slice of carbon is placed in a beam of electrons
so that the electrons diffract, producing diffraction rings which show their wave-like
properties
Probing Matter
• X-Ray Diffraction
A sample of the material is
placed in the beam of X-rays,
and the resulting scattering
pattern is picked up on a
photographic plate. The X rays
are diffracted in a cone. It is
useful tool to discover the
structure of solid materials.
Using a simple equation, the separation of layers of atoms can be determined:
n = 2d sin
where: n – order of diffraction  - de Broglie wavelength of the x-rays
d – the distance from source to screen  - diffraction angle (cone angle for this case)
Probing Matter
• Nuclear Radius
Rutherford estimated the radius
of a nucleus from his scattering
experiments, and using Coulomb’s
Law, to be ~ 3.0x10-14 m
The particle is repelled at point P.
It has zero Kinetic Energy, as it is
stationary; all its energy is potential.
Using electrostatic potential energy equations, the distance can be calculated:
Ep = potential at P × charge of the alpha particle:
Rearrange:
Therefore: rc
= 3.25x10-14 m
Probing Matter
• Electron Scattering
Electrons interact with the nucleus by electromagnetic interaction unlike the alpha
particles which interact by strong nuclear interaction.
A reasonable estimate can be obtained with a fairly simple equation:
where: λ - de Broglie wavelength of the high-energy electrons θ - angle of diffraction
R - nuclear radius
This gives a result of the radius being:
2.65 × 10-15 m
However, the radius depends on the nucleon number via a simple relationship:
R = r0 A 1/3
r0 - a constant, value: 1.4×10-15 m
A - nucleon number
The graph represents this
relationship between nuclear
radius and nucleon number
Nuclear radius is different to
atomic radius.
Atomic radius is similar
whether the element is light or
heavy.
Nuclear radius can vary
largely, depending on element
Summary
Basic Radioactivity
 Inverse Square Law of Gamma Radiation
 Exponential Law of Decay
 Probing Matter
