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Radioactive Decay Mechanisms
Many nuclei are stable. Many are radioactive or unstable, and will tend to decay by
emitting a particle, transforming the atom (made up of protons, neutrons and
electrons1) into an atom of another element, or into a lower energy state.
During radioactive decay, principles of conservation apply.




conservation of energy
conservation of momentum (linear and angular)
conservation of charge
conservation of nucleon number
In this document we consider four methods of radioactive decay; alpha, beta minus,
beta plus and electron capture. These may be accompanied by another emission called
gamma radiation. Note a nucleon is a general term that includes protons and neutrons.
Belt of Stability
If we plot the number of neutrons against the number of protons for all stable atoms we
get the following graph that is often referred to as the belt of stability.
Belt of stability. Neutron versus protons for stable isotopes
140
120
Z, number of neutrons
100
80
60
40
20
0
0
10
20
30
40
50
A, Number of protons
1
Atomic Structure and the Periodic Table
60
70
80
90
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Note that
1. there are no stable nuclei with an atomic number of 84 or greater.
2. for smaller atoms the ratio neutrons:protons is 1:1
3. for larger atoms the ratio of neutrons:protons approaches about 1.5:1
Since the strong nuclear force weakens significantly with distance, as the atom gets
bigger. If the number protons to neutrons remained in the ratio of 1:1 for larger atoms
then the repulsive force would be much stronger than the ‘strong force’. To compensate,
more neutrons are required to ‘pad out’ the nucleus to ensure its stability. One the
number of protons in the nucleus is above 83, no amount of extra neutrons can make
the nucleus stable.
Alpha Decay
Alpha decay is a Coulomb or electrostatic repulsion effect, which becomes more and
more disruptive as the size of the nuclei increase; overpowering the strong nuclear
force. In alpha decay, the nucleus emits an alpha particle; an alpha particle is essentially
a helium nucleus; a group of two protons and two neutrons. A helium nucleus is very
stable.
An example of an alpha decay involves uranium-238:
or
The process of transforming one element to another is known as transmutation. As a
result of alpha decay the mass number of the nuclide decreases by four units and the
atomic number reduces by two units (ie element shifts two places down the periodic
table. Note that elements with a high mass number tend to give off alpha radiation; they
need to significantly reduce their size to ever become stable.
Here are two further examples
Exercise: Write down the alpha decay equations for the following nuclides:
,
,
,
. Go to answers
Exercise: Write down the alpha decay equations for the following nuclides:
,
,
,
. Go to answers
,
,
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Beta Decay
A beta particle is either an electron or a positron, a positively-charged particle that is
the anti-matter equivalent of the electron. Hence there are two distinct types of beta
decay, the former is termed beta minus (β-) decay and the latter is termed beta plus (β+)
decay.
Beta minus decay
In beta minus decay a neutron converts into a proton and emits an electron. Hence the
atomic number increases by one and the mass number remains unchanged (ie the
element moves up one in the periodic table). For example
Where
can be written
and
represents an antineutrino (symbol ν
(Greek letter ‘nu’) represents a neutrino). Hence beta minus decay tends to occur when
the neutron to proton ratio is too high, that is that the isotope is above the stability belt.
Another example of beta minus decay is the decay of tritium
A further example of beta minus decay is the decay of
into
into
Exercise: Write down the beta minus decay equations for the following nuclides:
,
,
. Go to answers
,
Exercise: Write down the beta minus decay equations for the following nuclides:
,
,
,
. Go to answers
,
Beta plus or positron decay
Beta plus particles or positrons are the antimatter equivalent of beta minus particles.
Positron particles have the same mass as an electron, but it has a +1 charge. Beta plus
decay is the mirror image of beta decay in which a proton is converted into a neutron
and emits a positron. The atomic number goes down by one and mass number remains
unchanged. Beta plus decay tends to happen when the neutron to proton ratio is too
low.
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Here is an example of beta plus decay
where
is a neutrino.
Exercise: Write down the beta plus decay equations for the following nuclides:
,
,
. Go to answers
Exercise: Write down the beta plus decay equations for the following nuclides:
,
,
,
. Go to answers
,
,
Electron Capture
Electron capture is different to the other forms of decay in that it involves something
entering the nucleus, rather than being emitted from the nucleus. In electron capture an
electron from the lowest energy level falls into the nucleus and the other electrons
reorganise themselves into the normal shell structure. The negative electron combines
with one of the protons to become a neutron and another particle called a neutrino
(atomic number zero and mass number zero) is emitted. The atomic number is reduced
buy one and the mass number remains unchanged.
Here is an example of electron capture
Where e represents the electron, which can be written
, to show that it has the effect
of reducing the atomic number by one, but leaving the mass number unchanged.
Exercise: Write down the electron capture equations for the following nuclides:
,
,
. Go to answers
,
Exercise: Write down the electron capture equations for the following nuclides:
,
,
,
. Go to answers
,
Gamma radiation
Gamma radiation is often a by-product of alpha or beta radiation. Gamma radiation
allows the nucleus to remove surplus energy by the nucleus changes from a higher-level
energy state to a lower level. Similar to the energy levels for electrons in the atom, the
nucleus also has energy levels. The shells within the nucleus are less well understood
than the electron shells, but the energies involved with changes in the nuclear shells are
typically 1000000x greater than the energies involved with changes in the electron
shells.