# Decay equations

## Decay equations

To show what happens before and after a nuclear reaction (reaction involving the nucleus of an atom) we use equations that show both the proton (Z) and nucleon number (A). To balance a nuclear equation (left side and right side) you have to make sure that the sum of the nucleon (top) numbers on the left hand side equals the sum of the nucleon numbers on the right hand side AND the sum of the proton numbers on both sides also balance.

For Example:.

Top row = 18 on both the left and right sides.

Bottom row = 9 on both the left and right sides.

This is a balanced equation.

Nuclear equations such as these are useful for explaining what happens in radioactive decay processes.

Unstable nuclei emit alpha, beta or gamma radiation in order to become more stable.

As a result of emitting this radiation the character of the nucleus remaining is changed. This is radioactive decay.

The diagrams below show what happens when a nucleus emits alpha, beta or gamma radiation.

In alpha decay 2 protons and 2 neutrons are emitted. Notice that this reduces the nucleon number by 4 and the proton number by 2. A new element is thus formed.

In beta decay a neutron changes into a proton (which remains in the nucleus) and an electron (which is emitted as beta radiation). The net effect is an increase in proton number by 1, while the nucleon number stays the same. Again a new element is formed.

When a nucleus has undergone alpha or beta decay it is often left in a high-energy (excited) state. This energy can be lost in the form of an emitted a gamma ray. Because the composition of the nucleus is unchanged no new element is formed.

Here are 3 decay equations. Drag and drop the labels to check you understand the above information.

There are 2 forms of beta decay that occur: β+ decay and electron capture. In β+ decay a proton changes into neutron and emits a positron. This leads to a decrease in proton number, while the nucleon number stays the same. In electron capture a proton captures an electron from the orbiting cloud and changes into a neutron. Again this leads to a decrease in proton number but the nucleon number stays the same.

Diagram shows β+ and electron capture: