Questions: Beta Decay and the Weak Nuclear Force

Question 1

Alpha decay produces particles with discrete, fixed kinetic energies. Beta decay produces electrons with a continuous range of energies up to a maximum. What is the correct explanation for this difference?

• A. Electrons have mass while alpha particles are massless, so electrons can carry variable energy
• B. Beta decay is a three-body final state — the electron and antineutrino share the available energy variably, so neither has a fixed energy
• C. The weak force is inherently random in the energy it releases, unlike the strong force that drives alpha decay
• D. Beta particles lose variable energy to electromagnetic interactions as they exit the nucleus

Answer: (B)

This is the historical key insight that led Pauli to postulate the neutrino in 1930. Alpha decay is a two-body decay: nucleus → daughter + alpha particle. Two-body kinematics with conserved energy and momentum requires the alpha to have a single fixed energy. If beta decay were simply n → p + e⁻, the electron would also have a fixed energy. But experiments showed a continuous spectrum — electrons with all energies from zero to a maximum. The only resolution consistent with energy and momentum conservation is a third particle (the antineutrino) that carries away variable energy, making beta decay three-body.

Question 2

A nucleus has too many neutrons relative to protons and lies above the valley of stability on the binding energy landscape. Which decay mode would most directly move it toward stability?

• A. Alpha decay — it reduces both N and Z, lowering the neutron excess
• B. Beta-plus decay — converting a proton to a neutron would further increase the neutron count
• C. Beta-minus decay — converting a neutron to a proton reduces the neutron excess while leaving A unchanged
• D. Electron capture — it removes an electron from the atom, reducing the neutron count

Answer: (C)

Beta-minus decay converts a neutron to a proton (n → p + e⁻ + ν̄_e), reducing N by 1 and increasing Z by 1 while leaving the mass number A = N + Z unchanged. For a neutron-rich nucleus, this is exactly the transformation needed: it moves the nucleus toward the valley of stability by improving its N/Z ratio. Beta-plus decay does the opposite (p → n + e⁺ + ν_e), which would worsen the neutron excess. Electron capture also converts p → n, also worsening it. Alpha decay reduces both N and Z by 2, which might not improve N/Z efficiently.

Question 3

Beta decay changes the mass number A of a nucleus, while alpha decay does not.

• T. True
• F. False

Answer: False

This is precisely backwards. Alpha decay reduces A by 4 (losing two protons and two neutrons as a helium-4 nucleus). Beta decay does NOT change A — it converts a neutron into a proton (or vice versa), leaving the total nucleon count A = N + Z unchanged. Only Z changes (by ±1), which is why beta decay changes the element while leaving the isotope in the same mass region. This is the defining feature of beta decay: it adjusts the proton-neutron ratio without adding or removing nucleons.

Question 4

The existence of the neutrino was inferred from the continuous energy spectrum of beta decay electrons, because energy conservation requires that the 'missing' energy be carried away by an invisible particle.

• T. True
• F. False

Answer: True

Pauli's 1930 proposal was driven by energy and momentum accounting. If beta decay were two-body (n → p + e⁻), energy conservation would require the electron to have a single fixed kinetic energy, just as alpha particles do. Instead, electrons appeared with all energies from nearly zero to a maximum (Q-value), with the average around one-third of the maximum. The missing energy and momentum in each event had to go somewhere. Pauli proposed a very light, electrically neutral particle — the neutrino — that was undetectable but real. The neutrino was not directly detected until 1956 (Cowan-Reines experiment), but its existence was accepted long before on this indirect thermodynamic argument.

Question 5

Why did the continuous energy spectrum of beta decay electrons lead physicists to postulate the neutrino? What would the spectrum look like if the neutrino did not exist?

Model answer: If beta decay were a two-body process (n → p + e⁻), energy and momentum conservation in the rest frame of the decaying neutron would require the electron and proton to emerge with fixed, definite momenta — exactly as in alpha decay, which produces a sharp energy peak. Instead, experiments showed a broad, continuous distribution of electron energies up to a maximum. In any given decay, the electron could have anywhere from nearly zero to the full Q-value of kinetic energy. The 'missing' energy in each event had to go somewhere without being detected. Pauli proposed that a third particle — very light and electrically neutral — was emitted simultaneously, sharing the available energy variably with the electron. This three-body final state explains the continuous spectrum: in each decay, the electron and antineutrino share the energy in varying proportions, so neither has a fixed energy.

The neutrino postulate was driven entirely by conservation laws. Energy was apparently not conserved in two-body beta decay, which was deeply troubling. Rather than abandon conservation of energy (which Bohr seriously considered), Pauli proposed an undetectable particle as the carrier of the missing energy. This is a model example of inferring a new particle from indirect thermodynamic evidence before any direct detection.