Decay Equations (AQA A Level Physics): Revision Note

Changes in N and Z by Radioactive Decay

• There are four reasons why a nucleus might become unstable, and these determine which decay mode will occur

1. Too many neutrons = beta-minus emission

2. Too many protons = beta-plus emission or electron capture

3. Too many nucleons = alpha emission

4. Too much energy = gamma emission

If there are too many neutrons...

• Beta-minus (β^-) emission occurs

• One of the neutrons in the nucleus changes into a proton and a β^- particle (an electron) and antineutrino is released

• The nucleon number is constant

  • The neutron number (N) decreases by 1

  • The proton number (Z) increases by 1

• The general decay equation for β^- emission is:

${}_{\mathrm{Z}}{}^{\mathrm{A}}\mathrm{X}\to {}_{-1}{}^0\mathrm{\beta }+{}_{\mathrm{Z}+1}{}^{\mathrm{A}}\mathrm{Y}+{\overline{\mathit{v}}}_{\mathrm{e}}$

Representing beta-minus decay graphically

If there are too many protons...

• Beta-plus (β⁺) emission or electron capture occurs

• In beta-plus decay:

  • A proton changes into a neutron and a β⁺ particle (a positron) and neutrino are released

• In electron capture:

  • An orbiting electron is taken in by the nucleus and combined with a proton causing the formation of a neutron and neutrino

• In both types of decay, the nucleon number stays constant

  • The neutron number (N) increases by 1

  • The proton number (Z) decreases by 1

• The general decay equation for β⁺ emission is:

${}_{\mathrm{Z}}{}^{\mathrm{A}}\mathrm{X}\to {}_{+1}{}^0\mathrm{\beta }+{}_{\mathrm{Z}-1}{}^{\mathrm{A}}\mathrm{Y}+v_{\mathit{e}}$

Representing beta-plus decay graphically

• The decay equation for electron capture is:

${}_{\mathrm{Z}}{}^{\mathrm{A}}\mathrm{X}+{}_{-1}{}^0\mathrm{e}\to {}_{\mathrm{Z}-1}{}^{\mathrm{A}}\mathrm{Y}+v_e$

If there are too many nucleons...

• Alpha (α) emission occurs

• An α particle is a helium nucleus

• The nucleon number decreases by 4 and the proton number decreases by 2

  • The neutron number (N) decreases by 2

  • The proton number (Z) decreases by 2

• The general decay equation for α emission is:

${}_{\mathrm{Z}}{}^{\mathrm{A}}\mathrm{X}\to {}_2{}^4\mathrm{\alpha }+{}_{\mathrm{Z}-2}{}^{\mathrm{A}-4}\mathrm{Y}$

Representing alpha decay graphically

If there is too much energy...

• Gamma (γ) emission occurs

• A gamma particle is a high-energy electromagnetic radiation

• This usually occurs after a different type of decay, such as alpha or beta decay

• This is because the nucleus becomes excited and has excess energy

Representing Nuclear Processes Graphically

• In summary, alpha decay, beta decay and electron capture can be represented on an N–Z graph as follows:

Representing nuclear processes graphically