Alpha & Beta Decay (AQA A Level Physics): Revision Note

α & β decay equations

• When nuclei are unstable, they can become more stable through the process of radioactive decay

• Three of the most common decay mechanisms are:

  • Alpha decay

  • Beta-minus decay

  • Beta-plus decay

Alpha decay

• Alpha decay is common in large, unstable nuclei with too many nucleons (protons and neutrons)

• The decay involves a nucleus emitting an alpha particle and decaying into a different nucleus

• An alpha particle consists of 2 protons and 2 neutrons

  • This is equivalent to a helium nucleus

• When an unstable nucleus (the parent nucleus) emits radiation, the constitution of its nucleus changes

• As a result, the isotope will change into a different element (the daughter nucleus)

• Alpha decay can be represented by the following radioactive decay equation:

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

e.g. ${}_{84}{}^{212}\mathrm{Po}\to {}_{82}{}^{208}\mathrm{Pb}+{}_2{}^4\mathrm{\alpha }$

• When an alpha particle is emitted from a nucleus:

  • The nucleus loses 2 protons: proton number decreases by 2

  • The nucleus loses 4 nucleons: nucleon number decreases by 4

Beta-minus decay

• A beta-minus, β^-, particle is a high energy electron emitted from the nucleus

• β^- decay is when a neutron turns into a proton emitting an electron and an anti-electron neutrino

• When a β^- particle is emitted from a nucleus:

  • The number of protons increases by 1: proton number increases by 1

  • The total number of nucleons stays the same: nucleon number remains the same

${}_{\mathrm{Z}}{}^{\mathrm{A}}\mathrm{X}\to {}_{\mathrm{Z}+1}{}^{\mathrm{A}}\mathrm{Y}+{}_{-1}{}^0\mathrm{\beta }+{}_0{}^0\overline{\nu }_e$

e.g. ${}_6{}^{14}\mathrm{C}\to {}_7{}^{14}\mathrm{N}+{}_{-1}{}^0\mathrm{\beta }+{}_0{}^0\overline{\mathit{\nu }}_e$

• The new nucleus formed from the decay is called the 'daughter' nucleus (nitrogen in the example above)

Beta-plus decay

• A beta-plus, β⁺, particle is a high energy positron emitted from the nucleus

• β⁺ decay is when a proton turns into a neutron emitting a positron (anti-electron) and an electron neutrino

• When a β⁺ particle is emitted from a nucleus:

  • The number of protons decreases by 1: proton number decreases by 1

  • The total number of nucleons stays the same: nucleon number remains the same

${}_{\mathrm{Z}}{}^{\mathrm{A}}\mathrm{X}\to {}_{\mathrm{Z}-1}{}^{\mathrm{A}}\mathrm{Y}+{}_{+1}{}^0\mathrm{\beta }+{}_0{}^0\nu _e$

e.g. ${}_6{}^{10}\mathrm{C}\to {}_5{}^{10}\mathrm{B}+{}_{+1}{}^0\mathrm{\beta }+{}_0{}^0\nu _e$

Neutrino emission

• An electron neutrino is a type of subatomic particle with no charge and negligible mass which is also emitted from the nucleus

• The anti-neutrino is the antiparticle of a neutrino

  • Electron anti-neutrinos are produced during β^– decay

  • Electron neutrinos are produced during β⁺ decay

• Although the neutrino has no charge and negligible mass, its existence was hypothesised to account for the conservation of energy in beta decay

• When the number of α particles is plotted against kinetic energy, there are clear spikes that appear on the graph

• This demonstrates that α-particles have discrete energies (only certain values)

• When the number of β particles is plotted against kinetic energy, the graph shows a curve

• This demonstrates that beta particles (electrons or positrons) have a continuous range of energies

• This is because the energy released in beta decay is shared between the beta particles (electrons or positrons) and neutrinos (or anti-neutrinos)

• This was one of the first clues of the neutrino’s existence

• The principle of conservation of momentum and energy applies in both alpha and beta emission