Beta decay turns a neutron into a proton or a proton into a neutron, and shares the released energy Q between a beta particle and a neutrino. Pick one of eight real isotopes below, choose a decay mode, and fire decays one at a time to watch the continuous beta spectrum emerge from individual random events.
Beta Decay & the Beta Spectrum
Pick a real isotope, choose a decay mode, and fire decays one at a time. The nuclide chart shows where the daughter lands; the histogram below fills in with individually sampled electron energies until the continuous beta spectrum emerges.
What Is the Beta Decay Simulator?
The beta decay simulator is a free interactive physics lab that runs in your browser — nothing to install and no sign-up. Choose a real isotope, fire beta-minus, beta-plus or electron capture, and watch the true beta spectrum build up. It reports decay energy, this event · electron and Mean electron energy as you drag the sliders.
| Control | Range | Step |
|---|---|---|
| Nuclide | 1 – 8 | 1 |
How to Read What This Simulator Is Showing You
The Nuclide slider steps through eight real isotopes, and it changes more than a label. Each position loads that nuclide's true decay energy, its actual daughter product, and the modes physics allows it. Slide from tritium to sodium-22 and the endpoint marker travels almost the full chart, because one releases 18.6 keV and the other nearly a hundred times more. The squares above are a fragment of the chart of nuclides: gold is your parent, dark red is where it lands, and the arrow points up-left for beta-minus, down-right for beta-plus and electron capture.
Some mode buttons are greyed out, and that is a physical statement, not a limitation of the tool. Beta-plus must manufacture a positron and discard a surplus atomic electron, costing 1.022 MeV before anything is left for the products. A nuclide whose decay energy falls short simply cannot use that channel. Beryllium-7 is the instructive case: it decays happily by electron capture, which pays no such fee because the nucleus captures an electron that already exists, yet its beta-plus button never lights up. For the arithmetic behind those thresholds, the beta decay energy calculator works Q out from the atomic masses.
The histogram is what deserves your time, because it shows something no single number can. Fire one decay and you get one unremarkable value. Fire five hundred and a shape appears: a broad, lopsided hump rising from zero, peaking below the middle, tapering to the endpoint. Every event obeyed the same conservation law, yet no two split the energy alike, because an unseen neutrino took whatever the electron did not — the three-body split set out in beta decay explained. The running mean settles on the dashed grey line and stays there. For how fast a sample disappears rather than how hard it hits, see half-life.
That spread is the misconception this lab exists to correct. Tables quote carbon-14 at 156 keV and tritium at 18.6 keV, and it is natural to read those as the energy a beta carries. They are the maximum, reached only when the neutrino leaves with almost nothing; a typical beta gets roughly a third. Shielding, dose and detector calibration all depend on the real distribution, not its ceiling. Beta is also just one of three classical decay products, and the alpha, beta and gamma family behaves quite differently in each case.
Frequently asked questions
Why is the beta-plus button disabled for this isotope?
Because beta-plus decay costs 1.022 MeV before it can even start, and this isotope's decay energy does not cover it. Creating a positron takes one electron rest mass, and the daughter atom is left holding one electron too many, which it must shed — two rest masses at 0.511 MeV each. If the electron-capture Q-value is not above 1.022 MeV, the beta-plus channel is closed and the simulator greys the button out rather than letting you select a decay that cannot happen. Beryllium-7, with a Q of 0.8618 MeV, is the clearest case in the list.
Why do the electron energies differ every time I fire?
Because beta decay is a three-body split. The nucleus does not hand its energy to the electron alone — it shares it between the electron and an antineutrino (or neutrino), and the split is different in every single decay. Fire the same isotope twice and you get two different electron energies whose sum with the neutrino always comes to the same Q. That is exactly why the histogram builds into a smooth continuous curve rather than a single spike, and it is the observation that made Pauli propose the neutrino in the first place.
What does the endpoint marker mean?
It marks the maximum kinetic energy any electron from this decay can carry, which happens in the rare event where the neutrino takes essentially nothing. The endpoint equals the decay energy Q. Every sampled electron in the histogram falls to the left of that dashed line and none can cross it. Because the x-axis stays fixed while you change isotopes, the endpoint marker visibly slides right as you move to higher-energy emitters, which is the quickest way to compare two isotopes at a glance.
Where do the Q-values come from?
They are evaluated decay energies for real nuclides, taken from standard nuclear data rather than invented for the simulation. Each one is the difference between the parent and daughter atomic masses converted at 931.494 MeV per atomic mass unit, with 1.022 MeV subtracted for beta-plus. The eight isotopes in the slider are all ones you are likely to meet: carbon-14 and tritium for dating, potassium-40 for natural background, strontium-90 and iodine-131 from fission, and fluorine-18, sodium-22 and beryllium-7 on the proton-rich side.
Why does electron capture emit nothing I can see?
Because in electron capture there is no beta particle at all. The nucleus swallows one of its own atomic electrons instead of emitting one, so the only thing leaving is a neutrino — and a neutrino carries a single fixed energy rather than a spread, because with only two bodies in the final state the split is no longer free. That is why the histogram collapses from a broad continuous curve to one narrow line when you select EC. What laboratories actually detect from an electron-capture nuclide is the X-rays given off as the vacated electron shell refills.
References & formula source
- Krane — Introductory Nuclear Physics, chapter on beta decay (the allowed spectrum shape and Q-value definitions).
- Serway & Jewett — Physics for Scientists and Engineers, nuclear physics chapter (decay modes and disintegration energy).
- NNDC / Brookhaven National Laboratory — NuDat evaluated nuclear structure and decay data, the source of the Q-values used here.
- Further reading: Beta decay — Wikipedia