AQA A Level Physics

Revision Notes

8.3.1 Nuclear Instability

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
  • A nucleus will be unstable if it has:
    • Too many neutrons
    • Too many protons
    • Too many nucleons ie. too heavy
    • Too much energy
  • An unstable atom wants to become neutral to become stable

 

  • 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 very significant to the stability of nuclei
    • At a short-range (around 1–4 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-emitters:
    • Occur beneath the line of stability when Z > 60 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) emitters:
    • Occur 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+) emitters:
    • Occur 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:
    • 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

Exam Tip

To remember where the β and β+ emitters are on the graph:

  • Beta-minus is a negative particle where a neutron turns into a proton. Unstable atoms always want to go towards a roughly equal number of protons and neutrons
    • Therefore these emitters are on the neutron-rich side of isotopes
  • Beta-plus is a positive particle where a proton turns into a neutron
    • Therefore these emitters are on the proton-rich side of isotopes

The best way to remember the nuclear stability graph is to try to draw it from memory

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