Nuclear instability (A-level only): Graph of N against Z for stable nuclei.

The idea

A graph of neutron number N against proton number Z for stable nuclei shows a curved band called the line of stability. For light nuclei, the stable ratio N/Z is close to 1. As Z increases, Coulomb repulsion between protons grows, so more neutrons are needed to provide attractive strong nuclear force without adding charge; the line bends upwards, and the stable ratio rises to about 1.5 for heavy nuclei like lead-208. Nuclei above the band are neutron-rich and tend to undergo beta-minus decay. Nuclei below the band are proton-rich and tend to undergo beta-plus decay or electron capture. Very heavy nuclei beyond Z = 83 are unstable and primarily decay by alpha emission to reduce their size, though they can also undergo beta decays within decay chains to adjust their N/Z ratio.

What earns the marks

• Plot N on the vertical axis and Z on the horizontal axis, with stable nuclei forming a narrow curved band.
• State that light stable nuclei have N approximately equal to Z, giving a ratio close to 1.
• Explain that heavier stable nuclei need a higher N/Z ratio, up to about 1.5, because of increasing Coulomb repulsion between protons.
• Identify neutron-rich nuclei above the band as likely beta-minus emitters and proton-rich nuclei below the band as likely beta-plus emitters or electron capturers.
• Relate alpha emission of very heavy nuclei to overall instability beyond Z = 83, noting that beta decays also occur in heavy decay chains.
• Use the graph to predict a likely decay mode for a given nuclide from its position relative to the band.

Common mistakes and how to put them right

• Assuming the line of stability is straight with N = Z for all nuclei.

  Put it right: It curves upwards so heavy stable nuclei have more neutrons than protons.

• Thinking that any nucleus with N greater than Z is unstable.

  Put it right: Many light stable nuclei have N slightly greater than Z, and stability depends on the position relative to the band.

• Assuming heavy nuclei (Z > 83) only decay by alpha emission.

  Put it right: While alpha decay reduces overall mass, heavy nuclei also undergo beta decay to correct their N/Z ratio during decay chains.

Exam tips

• Sketch the axes with N vertical and Z horizontal and label the line of stability before adding any nuclide.
• Quote the approximate stable N/Z ratio for light and heavy nuclei to support your explanation.
• When predicting decay, state whether the nuclide is above or below the band and name the decay mode that moves it towards the band.