Decay Equations (Cambridge (CIE) A Level Physics): Revision Note

Neutrino emission

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

• The electron anti-neutrino is the antiparticle of an electron neutrino

  • Electron anti-neutrinos are produced during β– decay

  • Electron neutrinos are produced during β+ decay

Electron neutrino and anti-electron neutrino

The anti neutrino is denoted by a line above the symbol

α & β decay equations

Alpha decay

• Alpha decay is common in large, unstable nuclei with too many protons

• 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 (the nucleus of a Helium atom)

Alpha decay 

Alpha decay produces a daughter nucleus and an alpha particle (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:

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

• An example would be:

${}_{84}{}^{212}\mathrm{Po}\to {}_{82}{}^{208}\mathrm{Y}+{}_2{}^4\mathrm{\alpha }$

• 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

β^- decay

• A 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

Beta decay

In beta-minus decay, a neutron decays into a proton, an electron and an anti-electron neutrino

• When a β^- 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

• The decay equation for beta-minus decay is:

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

• An example would be:

${}_6{}^{14}\mathrm{C}\to {}_7{}^{14}\mathrm{N}+{}_{-1}{}^0\mathrm{\beta }+{}_0{}^0\overline{{\mathrm{v}}_{\mathrm{e}}}$

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

β⁺ decay

• A 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

Beta-plus decay

In beta plus decay, a proton decays into a neutron, a positron and an electron neutrino

• When a β⁺ 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

• The decay equation for beta-plus decay is:

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

• An example of this would be:

${}_6{}^6\mathrm{C}\to {}_5{}^6\mathrm{B}+{}_{+1}{}^0\mathrm{\beta }+{}_0{}^0\mathrm{v}_{\mathrm{e}}$

Energy of alpha & 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)

Graphs showing energy of alpha and beta particles

Alpha particles have discrete energy levels whilst beta particles have a continuous range of energies

• 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