Topic 4 – Variation  of N with Z for stable and unstable 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:

For stable nuclides, we notice the following:

• The lightest nuclides have almost equal numbers of protons and neutrons.

• The 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 protons.

• Most nuclides have both an even number of protons and an even number of neutrons. 

• Alpha particles are made of two protons and two neutrons.  Certain elements like silicon, oxygen, and iron have a similar ratio of protons and neutrons.

For unstable nuclides, we see:

• Disintegrations tend to produce new nuclides that are nearer the stability line, and carry on until the stability line is reached.

• Nuclides above the line decay so that the proton number increases by 1, i.e. a beta emission.

• Nuclides below the line decay to reduce the proton number and the proton to neutron ratio increases.  This is achieved by alpha decay.

·       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.

Possible modes of decay for unstable nuclei

Alpha radiation 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 Q stands for the energy.  The general decay equation is summarised below.

  We should note the following:

• The alpha particle is a helium nucleus (NOT atom)

• Energy 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.

• The velocity of the alpha particle is much greater than that of the nucleus.

• The nucleon number goes down by 4, the proton number by 2.

• A typical alpha decay is:

 

Question 1

Is this equation balanced?  Explain your answer.

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.

Neutron 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.

The 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 n_e (‘nu-bar e’) is a strange little particle called an electron antineutrino.  The general equation for b- decay is:

A typical decay is:

Notice that:

• The nucleon number remains the same ;

• The proton number goes up by 1.

• The 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.

• A precise amount of energy is released, according to the nuclide.

• That energy is shared among the nucleus, the electron and the antineutrino. 

The proportion of shared energy is variable, so there is a range of energies of the b- particles.  The graph shows a typical distribution.

If 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 radiation.

The 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 never occurs naturally, and is only 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:

Here we see a positively charged electron, the positron being emitted with an electron neutrino (n_e).  At the nucleon level we see:

The proton is turned into a neutron.

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:

And at the nucleon level we see:

Note 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 b- emission.

Excited Nuclei

After 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 ray (g-ray).  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.

Some points to note:

• The nucleus is unaltered physically.

• The radiation is about the same size of the nucleus, about 10^-14 m .

• The precise wavelength is a property of the nuclide involved.

• Gamma radiation causes little ionisation, so it’s very penetrating.

• Gamma rays are created at the instant of the decay.

The 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.

Gamma 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.

·      Tracers such as technetium-99 can be injected and used to monitor blood flow using a gamma camera.  This is an important diagnostic tool.