Nuclear Physics Tutorial
3 - Nuclear Instability
Stability of Nuclei
The chemical properties of any element are governed by the number of protons, the proton number, which is given the code Z. The stability of the nucleus depends on a combination of the proton number and the neutron number. We can plot a graph of the number of neutrons (given by the difference between the mass number and the proton number) against the proton number. The general pattern is like this:
This more detailed image has neutron number on the horizontal axis and the proton number on the vertical axis. Make sure that you make it clear on your own sketch graphs.
Image by Bdushaw - Own work, CC BY-SA 4.0, https://commons.wikimedia.org/w/index.php?curid=61302798
stable nuclides, we notice the
The lightest nuclides have almost equal numbers of protons and neutrons.
heavier nuclides require up to 50 % more neutrons than protons.
The greater number of neutrons is needed to stop the nucleus flying
apart, in effect diluting the repulsive force of the positively charged
nuclides have both an even number of protons and an even number of neutrons.
particles are made of two protons and two neutrons. Certain elements like silicon, oxygen, and iron have a
similar ratio of protons and neutrons.
unstable nuclides, we see:
tend to produce new nuclides that are nearer the stability line, and carry on
until the stability line is reached.
above the line decay so that the proton number increases by 1, i.e. a beta
below the line decay to reduce the proton number and the proton to neutron ratio
increases. This is achieved by
Beta plus decay also occurs where the nucleus is beneath the line of stability.
In this case a proton turns into a neutron and a positron
(positively charged anti-electron) is given off.
Common Modes of Decay - Alpha
mostly comes from heavy nuclides with proton numbers greater than 82, but
smaller nuclides deficient in neutrons can also be alpha emitters.
It is believed that the alpha particle is formed some time before its
emission, and it gains its energy from the mass
defect in the nucleus. The term
stands for the energy.
general decay equation is summarised below.
alpha particle is a helium nucleus
is released in the decay. The
quantity is precise, according to the nuclide.
The energy is kinetic,
with the majority going to the alpha particle and a little going to the
decayed nucleus. Some nuclides
emit all their alpha particles at one energy, while others emit them at two
or more discrete energy levels.
velocity of the alpha particle is much greater than that of the nucleus.
nucleon number goes down by 4,
the proton number by 2.
typical alpha decay is:
Is this equation balanced? Explain your answer.
Alpha particles are intensely ionising. They smash through air molecules, knocking off electrons as they go. However this reduces the kinetic energy, so that in the end they stop. Then they pick up a couple of free electrons to become helium atoms. To collect an appreciable sample of helium from an alpha emitter would take a very long time.
Common Modes of Decay - Beta Minus
rich nuclei tend to decay by beta minus (b-) emission.
The beta particle is a high-speed electron ejected from the nucleus, NOT
the electron clouds. It is formed
by the decay of neutrons, which are slightly more energetic than a proton.
Isolated protons are stable; isolated neutrons last about 10 minutes.
neutron, having emitted an electron, is converted to a proton, and this results
in the proton number of the nuclide going up by 1. A new element is formed.
The reaction at the nucleon level is:
Notice that as well as the neutron (n) and the proton (p), the beta particle is represented as an electron (e). The strange symbol:
(pronounced noo-bar e) is a strange little particle called an electron antineutrino. The
general equation for
b- decay is:
typical decay is:
nucleon number remains the same
proton number goes up by 1.
beta particle is created at the instant of the decay.
The antineutrino is very highly penetrating and has a tiny mass. It is very hard to detect, as it rarely interacts with matter.
The antineutrino has to be present to ensure that momentum is conserved.
precise amount of energy is released, according to the nuclide.
energy is shared among the nucleus, the electron and the antineutrino.
The neutrino was first proposed by Wolfgang Pauli (1900 - 1958) in about 1930 to explain how energy and momentum could be conserved in a beta minus decay. At that time the neutron was not yet discovered. (This was done in 1932 by James Chadwick (1891 - 1974).) The term neutrino ("neutral little thing") was coined by Enrico Fermi (1901 - 1954). Evidence was revealed by the way that the proton that was formed in the beta decay recoiled in a slightly different direction to that expected. The idea is shown below:
Conservation of momentum rules suggested that there must have been a third very tiny particle, which he called the neutrino (neutral little thing).
Later it was called the electron neutrino (as it was associated with an electron). However the use of quantum numbers showed that it must be an electron anti-neutrino.
The proportion of shared energy is variable, so there is a range of energies of the b- particles. The graph shows a typical distribution.
beta particles are emitted in a medium where the speed of light is lower than
that of the ejected electrons, then the passage of the electron is accompanied
by an optical shock wave, like the sonic boom of a supersonic aeroplane.
The resulting glow is called Cherenkov
is the balanced nuclear equation for the following decays?
emission of a beta- particle from oxygen 19
emission of an alpha particle from polonium 212
emission of a beta + particle from cobalt 56
Proton numbers O 8, F 9, Fe 26, Co 27, Pb 82, Po 84
Beta Plus Decay
positron is the anti-particle to the electron.
It has the same size, but opposite charge. Beta-plus (b+) decay involves the emission of a positron. It rarely occurs naturally, and is generally found in
nuclear physics experiments in reactors. If
we bombard fluorine atoms with alpha particles, we get a radioisotope of sodium,
which decays by positron emission.
The second reaction is:
we see a positively charged electron,
the positron being emitted with an electron
neutrino (ne). At the nucleon level we see:
The proton is turned into a neutron.
Is the charge conserved?
There is another way that a proton is turned into a neutron, and that is by electron capture. An electron is captured from the electron cloud. As another electron falls to take over the vacancy left, an X ray is emitted. The general scheme is:
at the nucleon level we see:
that prior to the emissions, the electrons, positrons, neutrinos, or
antineutrinos do not exist as separate entities within the nucleus.
They are created at the instant of the decay.
Free neutrons outside the nucleus decay to protons by
When radioisotopes decay, there may be several steps before the nucleus achieves stability. We call this series of decays a radioactive series or a decay chain. There are different half-lives at each step, some of which can be extremely long, while others are short. We can represent these graphically as shown below.
There are different permitted moves, according to the decays involved. Here is a decay chain.
We can show this series graphically.
Remember that the neutron number is not the same as the nucleon number.
Neutron number = nucleon number proton number
Note also that the emitted particle is NOT radioactive in itself.
alpha or beta decay, the daughter nucleus is often left in a very energetic
state. We call that state excited. The nucleus gets rid of this energy in the form of a photon
of electromagnetic radiation of very short wavelength, called a gamma
Gamma rays, cosmic rays, and hard X-rays have the same frequency, so are
really the same thing. Since
photons are not particles, there is no change in the proton number, or the
nucleon number. The nucleus becomes less energetic.
points to note:
nucleus is unaltered physically.
radiation is about the same size of the nucleus, about 10-14 m
precise wavelength is a property of the nuclide involved.
radiation causes little ionisation, so its very penetrating.
rays are created at the instant of the decay.
energy comes from the mass defect. At
the nuclear level the key idea is that mass and energy are interchangeable.
There is a measurable change in mass of a nuclide emitting gamma rays
over a long period.
rays have two important medical applications:
Radiotherapy a cobalt 60 source is aimed at a cancerous tumour.
The genetic material of cancers is generally unstable, and the gamma ray
photons can have sufficient interaction to render the cancerous cells unviable.
Unfortunately it can have the same effect on normal cells as well, and
there are nasty side effects.
such as technetium-99 can be injected and used to monitor blood flow using a
camera. This is an important diagnostic tool.
Explain how gamma rays are formed.
Energy levels in Nuclei
A nuclear event can be:
an alpha decay;
a beta minus decay;
a beta plus decay;
an electron capture event.
In any of these events, the daughter nucleus can be energetic. It can lose the excess energy by emitting a gamma photon. It then falls from the excited state to the ground state.
Consider this beta minus decay:
The aluminium nucleus is excited, and can be shown in an energy level diagram:
In this particular decay, there are three possible energies for the gamma photon. These are shown in the diagram as transitions.
Transition 1 is from 1.02 MeV to 0.83 MeV;
Transition 2 is from 0.83 MeV to 0 (the ground state);
Transition 3 is from 1.02 MeV to 0.
We can work out the energy of the gamma photon in joules by multiplying the energy by 1.6 Χ 10-19. Then we could work out the frequency of the photon by using the equation:
E = hf
It is possible for a daughter nucleus to remain in an excited state for some time. One example is the element technetium, formed by beta decay from a radioactive decay from an isotope of molybdenum.
This can be shown in an energy level diagram:
We refer to the prolonged excited state as metastable.
The technetium drops to ground state by emitting a gamma photon of 140 keV. This is low enough to be much safer than other gamma sources. The half life of the gamma emission is about 6 hours. Like all radioactive decays, the emission of gamma photons is random.
Technetium in its ground state decays by beta minus emission to ruthenium, with a half life of 211 000 years. This adds very little additional radiation burden on the body. Most of it is excreted in the urine.
The germanium isotope Germanium 77 has a metastable state which decays to the ground state by emission of a 0.16 MeV gamma photon. The isotope decays by beta minus emission to form an arsenic isotope which is in an excited state 0.48 MeV above the ground state. This is shown in the diagram below:
Other nuclides can be metastable, e.g.
Mn-46m; Ar-32m; Zn-69m