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Stable and unstable nuclei

A nucleus is a box of mutually repelling positive charges that somehow holds together. The force responsible works only at femtometre range, and when its balancing act fails, the nucleus rearranges itself by alpha or beta decay.

Year 12AQA 3.2.1.2

Builds on Constituents of the atom.

IN THIS TOPIC

  • Explain the role of the strong nuclear force, including its attractive and repulsive ranges.
  • Write balanced equations for alpha and beta-minus decay.
  • Explain why the neutrino was hypothesised from the beta-decay energy spectrum.

WHAT YOU PROBABLY THINK

Positive charges can never stick together.

The force that shouldn't need to exist

Every proton in a nucleus electrostatically repels every other, at separations where that repulsion is enormous. For nuclei to exist at all, something stronger must be gluing the nucleons together: the strong nuclear force, an attraction between nucleons that comfortably beats the electrostatic repulsion at nuclear range.

The strong nuclear force between nucleons: repulsive inside half a femtometre, attractive out to about three, gone beyondseparationforce0.5 fm3 fmrepulsionattractionbeyond 3 fm:negligible
FIG. 1The strong force between nucleons: fierce repulsion closer than about 0.5 fm, attraction from there out to about 3 fm, and nothing beyond.

Its defining feature is its reach. The attraction operates only out to about 3 fm; beyond that it vanishes, which is why the strong force plays no part in everyday life. Closer than about 0.5 fm it turns fiercely repulsive, which stops the nucleus collapsing to a point. Nucleons therefore sit at a comfortable spacing between the two limits, held in a force-balance pocket.

Alpha decay

Some nuclei, mostly very large ones, are unstable and rearrange themselves. In alpha decay the nucleus emits an alpha particle, a helium-4 nucleus: two protons and two neutrons in one tightly bound package. The bookkeeping: A falls by 4, Z falls by 2, and a new element results. Uranium-238 gives the standard example:

238U → 234Th + 4He, with the proton numbers balancing as 92 = 90 + 2.

Both numbers must balance across the arrow, always: nucleons are conserved and so is charge.

Beta decay, and the particle it demanded

In beta-minus decay a neutron inside the nucleus becomes a proton, emitting a fast electron (the beta particle) and a second, almost undetectable particle: the electron antineutrino, written as ν with a bar over it.

Beta-minus decay: inside the nucleus a neutron becomes a proton, emitting an electron and an electron antineutrinoneutronprotonelectronνelectron antineutrinoA is unchanged; Z rises by one
FIG. 2Beta-minus decay: a neutron becomes a proton, and an electron plus an electron antineutrino leave. A is unchanged; Z rises by one.

So A stays fixed while Z rises by one. Carbon-14 dating runs on exactly this: 14C → 14N + e− + an electron antineutrino, with 6 = 7 + (−1) + 0 balancing the charge.

The beta-decay energy spectrum: electrons emerge with a continuous range of energies, so something invisible carries the restelectron energycountexpected: all of the energyobserved: a continuous spreadthe antineutrino carries the missing energy
FIG. 3The beta energy spectrum: a continuous spread of electron energies, always short of the total available. The shortfall is the antineutrino's share.

The antineutrino was hypothesised before it was detected, to rescue conservation of energy. Each decay releases a fixed total energy, so if the electron were the only light product it would always carry the same energy. Instead, measured beta electrons show a continuous spectrum, from almost nothing up to the maximum. Either energy conservation fails, or an unseen partner carries the variable remainder. Pauli chose the partner, and decades later the neutrino was found, exactly as billed.

THE EXAM BIT

  • The strong-force numbers are quotable content: attraction out to about 3 fm, repulsion inside about 0.5 fm. Range questions want both, with the word “nucleons”, since the force acts on protons and neutrons alike.
  • Why does the nucleus not collapse? The very-short-range repulsion of the strong force. Why does it not fly apart? The strong attraction beats the electrostatic repulsion. Match the question to the correct half.
  • Decay equations are marked on the balancing: A and Z must each sum equally across the arrow, with the beta electron counted as Z = −1, A = 0.
  • Alpha: A down 4, Z down 2. Beta-minus: A unchanged, Z up 1. Stating the new element by name usually carries a mark.
  • The neutrino argument is an energy-conservation argument: continuous electron spectrum, fixed decay energy, therefore an undetected particle shares the total. Tell it in that order.

CHECK YOURSELF

Write the decay equation for radium-226 (Z = 88) undergoing alpha decay to radon (Rn), and check both balances.

Show a hint

The alpha particle takes four nucleons, two of them protons.

Show the answer

226Ra → 222Rn + 4He.

Nucleon check: 226 = 222 + 4. Proton check: 88 = 86 + 2, so radon has Z = 86.

Both books balance, and the element changed because Z changed: that is what decay does.

The strong force holds the nucleus, out to 3 fm.

Every decay balances A and Z exactly.

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