When physicists measured the energy of beta particles, they hit a puzzle that shook the subject: the energy wasn’t fixed. Alpha particles came out with sharp, exact energies — but beta particles emerged with a whole continuous range. Energy seemed to be going missing. Rather than abandon the law of conservation of energy, physicists proposed a ghostly, almost undetectable particle carrying the missing energy away: the neutrino. It was a prediction made purely to save conservation — and it turned out to be right.
📚 What you need to know
A neutrino is a subatomic particle with no charge and negligible mass, emitted from the nucleus
The antineutrino is its antiparticle; both are extremely hard to detect
Antineutrinos are emitted in beta-minus decay; neutrinos in beta-plus decay
Alpha particles are emitted with discrete (specific) energies
Beta particles are emitted with a continuous range of energies
The neutrino was proposed to explain the beta energy spectrum — it carries away the missing energy
Energy and momentum are conserved in both alpha and beta decay
The puzzle: two very different spectra
When you plot the number of particles emitted against their kinetic energy, alpha and beta decay look completely different:
Alpha particles come out at fixed energies (sharp spikes), but beta particles show a continuous spread up to a maximum. The beta case looked like energy was going missing.
Alpha: discrete energies (as expected)
Alpha decay obeys conservation neatly. The nucleus drops between fixed energy levels, so the alpha particle always carries a specific amount of energy — giving those sharp spikes. This is exactly what you’d expect if energy is conserved between two discrete states.
Beta: a continuous range (the problem)
Beta decay was baffling. If a neutron simply becomes a proton plus an electron, the electron should always come out with the same fixed energy — a single spike, like alpha. Instead, beta particles emerged with every energy from zero up to a maximum. Most came out with less than expected. Where was the rest of the energy going?
This was a genuine crisis. The measured beta energy almost never matched what conservation of energy demanded — it was nearly always short. Some physicists were so troubled they wondered if energy conservation itself might break down inside the nucleus. The bolder move, made by Wolfgang Pauli, was to trust conservation completely and conclude that an unseen particle must be sneaking off with the balance.
The solution: an invisible particle
The fix was to propose a new particle — the neutrino (or its antiparticle, the antineutrino) — emitted alongside the beta particle. It has no charge and negligible mass, which is why it slips through detectors almost unnoticed. Crucially, it shares the decay energy with the beta particle:
When the neutrino takes a little energy, the beta particle gets most — a high-energy beta.
When the neutrino takes a lot, the beta particle gets little — a low-energy beta.
The two shares always add up to the same fixed total.
This explains the continuous spectrum perfectly: the beta particle’s energy varies because it’s splitting a fixed amount with an invisible partner, in every possible ratio.
Fixed decay energy
shared between
Beta particle
+
(anti) neutrino
The neutrino is the reason beta energy comes out as a range: the total is fixed, but how it’s divided between the electron and the neutrino varies from decay to decay. Sometimes the electron hogs it, sometimes the neutrino does. Add the two back together and energy conservation is perfectly restored — which is exactly why the particle had to exist. Its later direct detection confirmed the prediction.
Which particle in which decay?
Beta-minus and beta-plus decay emit different members of the neutrino family. Recalling the underlying changes:
Neutrinos in beta decaybeta-minus: n → p + e− + antineutrino (v̄e)beta-plus: p → n + e+ + neutrino (ve)
WE 1
Explain why the continuous energy spectrum of beta particles provided evidence for the existence of the neutrino.
Step 1 — what was expected
If only a beta particle were emitted, it should carry a fixed energy (a single spike).
Step 2 — what was observed
Beta particles came out with a continuous range, mostly less than the maximum.
Step 3 — the conclusion
The missing energy must be carried by an unseen particle sharing the energy.
A neutrino was proposed to conserve energyThe logic chain: expected a fixed energy, saw a range, so energy was “missing” → an invisible particle (the neutrino) must carry it, preserving conservation of energy.
WE 2
State which particle — a neutrino or antineutrino — is emitted in beta-minus decay, and give the two properties that make it so hard to detect.
Step 1 — which particle?
Beta-minus decay (n → p + e−) emits an antineutrino.
Step 2 — why hard to detect?
It has no charge and negligible mass.
Antineutrino; no charge and negligible massBeta-minus → antineutrino; beta-plus → neutrino. Its lack of charge means it ignores electric and magnetic fields, and its tiny mass means it barely interacts with matter — so it’s almost invisible.
⚛ Answering a neutrino question
Why proposed? Beta energy was a continuous range, so energy seemed missing.
What restores it? An unseen particle sharing the fixed decay energy.
Which particle? Beta-minus → antineutrino; beta-plus → neutrino.
Why undetectable? No charge, negligible mass.
Alpha vs beta spectrum? Alpha discrete; beta continuous.
💡 Top tips
Alpha spectra are discrete; beta spectra are continuous.
The neutrino was proposed to conserve energy in beta decay.
Beta-minus → antineutrino; beta-plus → neutrino.
It’s hard to detect because it has no charge and negligible mass.
The fixed energy is shared between the beta particle and the neutrino.
⚠ Common mistakes
Saying beta particles have discrete energies — that’s alpha
Swapping neutrino and antineutrino between beta-plus and beta-minus
Claiming energy is not conserved in beta decay — it is, via the neutrino
Giving the neutrino a charge — it has none
Forgetting the energy is shared, which is what makes beta continuous
Quick recap:Alpha particles have discrete energies, but beta particles have a continuous range — energy seemed to go missing. The neutrino (no charge, negligible mass) was proposed to carry the balance away and conserve energy. Beta-minus emits an antineutrino; beta-plus emits a neutrino. The fixed decay energy is shared between the beta particle and the (anti)neutrino, giving the continuous spectrum.
That completes the whole Radioactivity & Decay story — from what isotopes are, through the three radiations and their equations, half-life and the decay law, the applications, and finally the deep nuclear ideas of binding energy, stability, energy levels and the neutrino. From here the course moves into fission and fusion reactors and the wider world of particle physics, where the neutrino you just met becomes one character in a whole zoo of fundamental particles.
The neutrino evidence not quite landing?
Book a free meeting and we’ll drill the alpha-vs-beta spectrum, the energy-conservation argument, and neutrino vs antineutrino.
