Nuclear Instability (AQA A Level Physics)

• The most common elements in the universe all tend to have values of N and Z less than 20 (plus iron which has Z = 26, N = 30)
• Where:
  • N = number of neutrons
  • Z = number of protons / atomic number

• This is because lighter elements (with fewer protons) tend to be much more stable than heavier ones (with many protons)
• Nuclear stability becomes vastly clearer when viewed on a graph of N against Z

This nuclear stability curve shows the line of stable isotopes and which unstable isotopes will emit alpha or beta particles

• A nucleus will be unstable if it has:
  • Too many neutrons
  • Too many protons
  • Too many nucleons ie. too heavy
  • Too much energy

• For light isotopes, Z < 20:
  • All these nuclei tend to be very stable
  • They follow the straight-line N = Z

• For heavy isotopes, Z > 20:
  • The neutron-proton ratio increases
  • Stable nuclei must have more neutrons than protons

• This imbalance in the neutron-proton ratio is significant to the stability of nuclei
  • At a short range (around 1–3 fm), nucleons are bound by the strong nuclear force
  • Below 1 fm, the strong nuclear force is repulsive in order to prevent the nucleus from collapsing
  • At longer ranges, the electromagnetic force acts between protons, so more protons cause more instability
  • Therefore, as more protons are added to the nucleus, more neutrons are needed to add distance between protons to reduce the electrostatic repulsion
  • Also, the extra neutrons increase the amount of binding force which helps to bind the nucleons together

• The graph of N against Z is useful in determining which isotopes will decay via
  • Alpha emission
  • Beta-minus (β^-) emission
  • Beta-plus (β⁺) emission
  • Electron capture

Alpha emission

• Alpha emitters are found beneath the line of stability when Z > 82 where there are too many nucleons in the nucleus
• These nuclei have more neutrons than protons, but they are too large to be stable
• This is because the strong nuclear force between the nucleons is unable to overcome the electrostatic force of repulsion between the protons

Beta-minus (β^-) emission

• Beta-minus emitters are found to the left of the stability line where the isotopes are neutron-rich compared to stable isotopes
• A neutron is converted to a proton and emits a β^– particle (and an anti-electron neutrino)

Beta-plus (β⁺) emission

• Beta-plus emitters are found to the right of the stability line where the isotopes are proton-rich compared to stable isotopes
• A proton is converted to a neutron and emits a β⁺ particle (and an electron neutrino)

Electron capture

• Electron capture occurs when a nucleus captures one of its own orbiting electrons
• As with β⁺ decay, a proton in the nucleus is converted into a neutron, releasing a gamma-ray (and an electron neutrino)
• Hence, this also occurs to the right of the stability line where the isotopes are proton-rich compared to stable isotopes