Physics › Particles › Stable and unstable nuclei
Stable and unstable nuclei
Inside a nucleus the strong nuclear force attracts nucleons out to about 3 fm, and closer than about 0.5 fm it becomes repulsive. Where it cannot balance the electrostatic repulsion between protons, the nucleus decays by alpha emission; a nucleus with too many neutrons decays by beta-minus emission. The continuous beta energy spectrum is why the antineutrino was proposed.
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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.
COMMON MISCONCEPTION
Positive charges can never stick together.
Protons do repel electrically, but within about 3 fm the strong nuclear force is attractive and overpowers that repulsion, holding the nucleons of a nucleus together.
The strong nuclear force
At separations of a few femtometres, the strong nuclear force provides an attraction that exceeds the electrostatic repulsion between protons. It acts between nucleons, protons and neutrons alike, and it is what allows a nucleus of mutually repelling protons to hold together.
Its defining feature is its range. The attraction acts between about 0.5 fm and about 3 fm and is negligible beyond, so the strong force has no effect at everyday distances. Closer than about 0.5 fm it becomes repulsive, which is what stops a nucleus collapsing. Nucleons settle at a separation between the two limits, where the attraction and the short-range repulsion balance.
Alpha decay
Some nuclei, mostly very large ones, are unstable and rearrange themselves. In alpha decay the nucleus emits an alpha particle, which is a helium-4 nucleus, two protons and two neutrons in one tightly bound package. 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, because 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, along with a second and almost undetectable particle, the electron antineutrino, written as ν with a bar over it.
So A stays fixed while Z rises by one. Carbon-14 dating runs on exactly this decay, 14C → 14N + e− + an electron antineutrino, with 6 = 7 + (−1) + 0 balancing the charge.
The antineutrino was hypothesised before it was detected, to rescue conservation of energy. Each decay releases a fixed total energy, so an electron leaving alone would always carry the same amount. Measured beta electrons do nothing of the kind. They show a continuous spectrum, from almost nothing up to a maximum. Either energy conservation fails, or an undetected particle carries the variable remainder. Pauli proposed the particle in 1930; the neutrino was detected experimentally in 1956. In beta decay the antineutrino carries energy and momentum so that both are conserved.
WORKED EXAMPLE
Writing a beta-minus equation
Carbon-14 (Z = 6) undergoes β− decay. Write the full equation and check that it balances.
β− turns a neutron into a proton, so A stays put, Z rises by one, and the electron leaves with an electron antineutrino.
14C → 14N + e− + e, with nitrogen at Z = 7.
Now check both totals. Nucleons, 14 = 14 + 0 + 0. Charge, 6 = 7 + (−1) + 0. The antineutrino carries the energy the electron does not, which is how it was predicted in the first place.
GUIDED PRACTICE
Thorium takes its turn
Thorium-234 (Z = 90) undergoes β− decay to protactinium (Pa). Write the equation and check both balances.
Show the working
234Th → 234Pa + e− + e, with Pa at Z = 91.
Nucleons, 234 = 234 + 0 + 0. Charge, 90 = 91 − 1 + 0. The daughter has moved one place right in the periodic table while its mass number is unchanged, and that pairing identifies β−.
INDEPENDENT PRACTICE
Predicting the decay mode
A nuclide has significantly more neutrons than its stable neighbours. Predict its likely decay mode, and what the decay does to its neutron and proton counts.
Show the working
Neutron-rich nuclei correct themselves by β− decay, turning one neutron into a proton.
N falls by one, Z rises by one, and the nuclide steps diagonally towards the stable band. The N against Z map in the nuclear unit draws that step in exactly those terms.
ASSESSMENT FOCUS
- The strong-force numbers are quotable content. Attraction out to about 3 fm, repulsion inside about 0.5 fm. Range questions want both, and they want the word “nucleons”, because the force acts on protons and neutrons alike.
- Why does the nucleus not collapse? The very-short-range repulsion. Why does it not fly apart? The strong attraction beats the electrostatic repulsion. Two questions, two different halves of the same graph.
- Decay equations are marked on the balancing. A and Z must each sum equally across the arrow, with the beta electron counted as A = 0 and Z = −1.
- Alpha takes A down by 4 and Z down by 2. Beta-minus leaves A alone and takes Z up by 1. Name the daughter element as well as writing the numbers.
- The neutrino argument is an energy-conservation argument, and the order matters. Continuous electron spectrum, fixed decay energy, therefore an undetected particle takes the rest.
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.
Nucleons balance, 226 = 222 + 4. Protons balance, 88 = 86 + 2, so radon sits at Z = 86.
Both totals hold, and the element changed because Z changed.
The strong force attracts out to 3 fm and repels inside 0.5 fm.
Every decay balances A and Z exactly.
The antineutrino exists because the beta spectrum is continuous.
WORKBOOK
Printable practice for this topic: original exam-style questions with room to work, and a fully worked answer book. Free to use; please do not redistribute or sell.
Or read them with their mark schemes on the stable and unstable nuclei questions page.
USED LATER IN
CHECK YOUR PROGRESS
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- 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.
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