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:

  • too many neutrons = beta-minus emission

  • too many protons = beta-plus emission or electron capture

  • too many nucleons = alpha emission

  • too much energy = gamma emission

If there are too many neutrons...

• Beta-minus (${\beta }^{-}$) emission occurs

• One of the neutrons in the nucleus changes into a proton and a ${\beta }^{-}$ 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 ${\beta }^{-}$ emission is:

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

If there are too many protons...

• Beta-plus (${\beta }^{+}$) emission or electron capture occurs

• In beta-plus decay:

  • A proton changes into a neutron and a ${\beta }^{+}$ 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 ${\beta }^{+}$ emission is:

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

• 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 ($\alpha$) emission occurs

• An $\alpha$ 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 $\alpha$ emission is:

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

If there is too much energy...

• Gamma ($\gamma$) 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: