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2. Isotopes and decay page 9
Decay equations
We can plot stable isotopes on a graph of number of neutrons (N) against number of protons (Z). The nuclei that do not lie on the line of stability have the wrong make-up to be stable. They may have too many neutrons or too few, or they may just be too big. These unstable nuclei emit radiation to try to turn themselves into something more stable.

By giving out radiation, the composition of the nucleus changes. It will turn into the nucleus of a different element! We saw on page 7 that there are three main types of radiation: alpha (a), beta (b) and gamma (g). Let's see which isotopes tend to give out each type of radiation and what happens when they decay.

N Z plot of stable isotopes
Picture 2.12 Regions of alpha decay.
What happens in alpha decay?
When a nucleus decays by alpha emission, it gives out a helium nucleus. The symbol for this is:

            Alpha  or  Alpha

We can find out what happens when an isotope decays by writing a balanced equation for the decay. For example, polonium–212 decays by alpha emission. We can write an equation for the decay as follows:

           Alpha decay

Notice that the mass number on the left hand side equals the sum of the mass numbers on the right. Similarly, the number of protons balances on each side of the equation.

If we know what leaves the nucleus, w can work out what it changes into. In this case, we know that the daughter product must be lead because, in order to make the equation balance, the daughter must have 82 protons. The element with atomic number 82 is lead.

When do we get alpha decay?
A nucleus decays because it is unstable. The daughter nucleus will be more stable than the parent (or closer to stability). When a nucleus decays by alpha radiation, the number of neutrons goes down by 2 and so does the number of protons. If we plot this change on the graph of N against Z, it is a straight line with a gradient of 1. For alpha-emitters, this line will take them closer to the line of stability.

There are two connected regions of nuclei that decay by alpha emission. Let's have a look at them and why they tend to give out alpha particles.

Region Reason
Nuclei that have more than 82 protons in them (too many to ever be stable) Rather like a bishop's chess move, the diagonal move on the N-Z plot quickly takes the heavy nucleus back towards Z = 82 and the line of stability.
Some heavy nuclei close to the N=Z line will decay by alpha emission. The gradient of the line of stability is about 1.5 in this region. By moving down with a shallower gradient (of 1), the nucleus is heading towards the line of stability.
What happens in beta minus decay?
Lighter nuclei generally decay by beta emission. There are two types of beta radiation: beta minus (b-) and beta plus (see below).

We can write an equation for beta minus decay. But first, let's see what symbol we will use for the electron. In beta minus decay, a neutron turns into a proton and gives out a fast moving electron. This gives us a clue on how to represent a beta particle in a decay equation.

                    (Note this isn't the comlete equation – see page 16.)

We need to consider three quantities:

Quantity Balancing
Charge The charges on the proton and electron balance to give a zero net charge on the right (this balances with the neutral neutron on the left).
Atomic mass number The proton and the neutron have the same atomic mass number. So the electron has an atomic mass number of 0. This doesn't mean that it has zero mass but that it doesn't contain any nucleons; and its mass is so much smaller than that of the nucleons that this doesn't cause a problem.
Atomic number The atomic number of a proton is 1 (it contains 1 proton) and of a neutron is zero (it contains no protons). In order to balance the equation, the electron has an atomic number of -1.

So the nuclear symbol for a beta minus particle is: (Sometimes, the minus is left off.)

N Z plot of stable isotopes
Picture 2.13 Graph of stable isotopes showing region of beta minus and beta plus decay.
When do we get beta minus decay?
In b- radiation, the nucleus loses a neutron and gains a proton. This makes it move down and to the right on the graph. Beta minus emitters are therefore on the left of the line of stability. They tend to have too many neutrons. Beta decay takes them towards the line of stability when a neutron turns into a proton.

For example, carbon-14 is a radioactive isotope of carbon. It decays by beta minus emission. The equation for this decay is:

           

Notice that the atomic mass number is unchanged (because a neutron changed into a proton) and that the atomic number has gone up by one (it has gained a proton).

Beta plus decay
Beta plus decay happens when a proton changes into a neutron, giving out a positron.

                    (Note this isn't the comlete equation – see page 16.)

The positron is a particle of antimatter that carries a single positive charge. It has an atomic number of 1 and zero atomic mass number (for similar reasons to those shown for the beta minus particle above). An isolated proton is stable and does not decay. However, when it is a part of a nucleus with too many protons, it can decay to form a neutron – reducing the atomic number by one and leaving the mass number unchanged. The effect is a single move up and to the left on the graph of stability. Therefore, beta plus decay happens to nuclei on the right of the line (those with too few neutrons to be stable).

An example of beta plus decay is the isotope nitrogen-12, which has too few neutrons. If a proton changes into a neutron, giving out a beta plus particle, the nucleus becomes one of carbon-12, which is extremely stable.

           

Gamma
Gamma radiation quite often accompanies either alpha or beta radiation to allow the nucleus to get rid of any surplus energy. In radioactive decay, the daughter nucleus might be created in an excited state (similar to the excited states of atoms that lead to them giving out visible and near visible light). When the daughter nucleus returns to its ground state, it releases energy by giving out radiation. The amounts of energy are about a million times greater than those involved in atomic transitions. So the radiation has a much higher frequency - in the gamma part of the spectrum.
Question 8
For each of the isotopes below, state which type of decay they are likely to undergo.

a) phosphorous-32 (Z = 15, phosphorous-31 is stable)

b) phosphorous-30

c) uranium-233

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