Nuclear Instability (AQA A Level Physics): Revision Note

Nuclear Stability Graph

• 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, i.e., 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

Alpha, Beta & Electron Capture

• 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 typically heavy nuclei found in the region Z > 82, beyond the end of the line of stability

  • They have too many nucleons in the nucleus to remain stable

• Like all heavy nuclei, alpha emitters have more neutrons than protons

  • For example, uranium-238 has 92 protons and 146 neutrons

• These nuclei are unstable because the strong nuclear force is short-range and cannot bind nucleons across the whole large nucleus

  • Meanwhile, the long-range electrostatic repulsion between protons acts across the entire nucleus

• Emitting an alpha particle (2 protons + 2 neutrons) reduces both the proton count and the total nucleon count, moving the nucleus closer to the line of stability

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