Beta decay is a radioactive process in which an unstable nucleus turns a neutron into a proton, or a proton into a neutron, emitting a fast electron or positron together with a neutrino. The mass number stays the same while the atomic number shifts by one. The weak nuclear force drives it.
Eat a banana and you swallow a tiny radioactive source. Roughly one potassium atom in every 8,500 is potassium-40, and inside your body about 4,000 of those nuclei fall apart every second — the overwhelming majority by beta decay.
You feel nothing. But that same process dates the charcoal in an Ice Age hearth, lights the emergency signs above aeroplane doors, and lets a PET scanner find a tumour years before you would notice it. One nuclear trick, running quietly everywhere.
What Is Beta Decay?
Beta decay is the transformation of a nucleus in which a neutron becomes a proton, or a proton becomes a neutron, with a high-speed electron or positron ejected to balance charge. The nucleus keeps the same number of nucleons but changes element.
Think of a nucleus as a ledger with two columns: protons and neutrons. Stability depends on the ratio between them, not the total. A nucleus can hold exactly the right number of nucleons and still be unstable — because they are sorted into the wrong columns.
Beta decay is the accountant. It moves one nucleon from the neutron column to the proton column, or the other way, until the ratio sits closer to the stable band. Nothing leaves the nucleus except the light particles that carry off charge and energy.
The Particle Everyone Gets Wrong
Here is the part that trips up almost every student. The emitted electron was never inside the nucleus.
Nuclei contain protons and neutrons — no electrons. The beta particle is manufactured at the instant of decay, created out of the energy released when the neutron converts. It is an electron in every measurable respect, but it has no history before that moment.
The Beta Decay Formula and Equations
The core equation is the decay of a single neutron, and every beta-minus event in every nucleus is a version of it:
Written for a whole nucleus, with X the parent and Y the daughter:
Two conservation rules do all the bookkeeping. The mass number A is unchanged; the atomic number Z rises by one, because a neutral neutron has become a positive proton while a negative electron departs.
| Symbol | Quantity | SI unit |
|---|---|---|
| A | Mass number (protons + neutrons) | dimensionless |
| Z | Atomic number (proton count) | dimensionless |
| e− | Beta particle (electron), charge −1.602 × 10−19 C | coulomb (C) |
| ν̄e | Electron antineutrino (neutral, near-zero mass) | — |
| Q | Decay energy released, shared by the products | joule (J); usually quoted in MeV |
Working Out the Decay Energy
The energy released is called the Q-value, and it comes straight from the mass difference between parent and daughter. Using atomic masses, the electron masses cancel automatically for beta-minus:
For beta-plus decay you must subtract two electron masses, because the parent atom sheds one orbital electron while the nucleus creates a positron:
These are the standard relations used in evaluated nuclear data; the National Nuclear Data Center publishes measured Q-values for every known nuclide on exactly this basis.
Convert mass to energy with 1 u = 931.494 MeV/c2. A convenient shortcut: 2mec2 = 1.022 MeV, a number that turns out to decide whether beta-plus decay can happen at all. If mass-energy equivalence is new to you, that conversion is the whole idea in one line.
The Three Types of Beta Decay
There are three types of beta decay: beta-minus, beta-plus and electron capture. All three change Z by one while leaving A untouched, and all three are driven by the same weak interaction.
Beta-Minus (β−): Too Many Neutrons
A neutron converts to a proton, throwing out an electron and an electron antineutrino. This is the common case — most nuclei made in reactors and in stellar nucleosynthesis are neutron-rich, and beta-minus is how they climb back toward stability.
Beta-Plus (β+): Too Many Protons
A proton converts to a neutron, emitting a positron and a neutrino. The positron is antimatter: it survives a few millimetres in tissue, meets an electron, and both vanish into two 511 keV gamma photons. That annihilation signature is exactly what a PET scanner detects.
Beta-plus has a hard energy threshold. The nucleus must supply the rest mass of the new positron and pay back the orbital electron the atom loses — 1.022 MeV in total. Below that, it simply cannot happen.
Electron Capture: The Quiet Alternative
A proton-rich nucleus with less than 1.022 MeV to spend has one route left. It reaches out and swallows one of its own inner orbital electrons, converting a proton to a neutron and emitting a single neutrino.
Nothing charged comes out, so electron capture is easy to miss. The giveaway is the X-ray emitted moments later, when an outer electron drops down to fill the vacated inner shell.
| Feature | Beta-minus (β−) | Beta-plus (β+) | Electron capture |
|---|---|---|---|
| Nucleon change | n → p | p → n | p + e− → n |
| Emitted particles | Electron + antineutrino | Positron + neutrino | Neutrino only, then X-rays |
| Atomic number Z | +1 | −1 | −1 |
| Mass number A | Unchanged | Unchanged | Unchanged |
| Triggered by | Neutron excess | Proton excess | Proton excess |
| Energy threshold | Any Q > 0 | Needs 1.022 MeV | No 1.022 MeV threshold |
| Typical example | Carbon-14 | Fluorine-18 | Beryllium-7 |
How Beta Decay Works Inside the Nucleus
Beta decay works because one quark inside a neutron changes flavour, mediated by the weak force. Go one level below protons and neutrons and the process becomes almost simple.
A neutron is two down quarks and one up quark (udd). A proton is two up quarks and one down quark (uud). The difference between them is a single quark.
In beta-minus decay, one down quark emits a W− boson and becomes an up quark. The W− is enormously heavy — about 80 GeV/c2, some 85 times the mass of the whole neutron — so it can exist only for the fleeting interval quantum mechanics allows, then immediately splits into the electron and the antineutrino we detect.
How long a free neutron actually lasts is still an open question. Two techniques — counting surviving neutrons in a bottle, and counting the protons produced in a beam — disagree by about nine seconds, far more than their stated uncertainties, and NIST notes the discrepancy is not yet understood.
Nine seconds out of nine hundred sounds trivial. It is not: the neutron lifetime feeds directly into predictions of how much helium the Big Bang produced, so the gap is being chased hard.
That absurd mass mismatch is why beta decay is slow. The weak force earns its name here: a free neutron survives about 15 minutes on average, while decays governed by the strong force finish in less than 10−22 seconds. Curious about the quarks themselves? Our guide to quarks and the Standard Model unpacks the full particle family.
Why Beta Particles Come Out at Every Energy
Beta particles emerge with a continuous spread of energies, from almost zero up to a sharp maximum called the endpoint, because the decay energy is shared randomly between the beta particle and the neutrino. Alpha and gamma emissions, by contrast, come in sharp lines.
This looked like a catastrophe when it was discovered. If a nucleus with a fixed mass decays to a daughter with a fixed mass, the released energy is fixed too — so every electron should carry the same amount. Instead, almost all of them carried less.
Energy appeared to be vanishing. Some physicists were ready to abandon conservation of energy inside the nucleus altogether.
In 1930 Wolfgang Pauli proposed a desperate fix: an unseen, neutral, nearly massless particle leaving with the missing energy. He called it a desperate remedy, and worried he had invented something nobody would ever be able to detect. Enrico Fermi built it into a working theory of beta decay and named it the neutrino.
It took until 1956 for Clyde Cowan and Frederick Reines to catch antineutrinos streaming from a nuclear reactor. Pauli’s undetectable particle had been real for twenty-six years.
In practice this matters for shielding. Quoted beta energies are endpoint values, not typical ones — the average beta particle leaves with only about a third of the endpoint energy, because the neutrino takes the rest.
Real-World Examples of Beta Decay
Beta decay shows up in archaeology, medicine, geology and your own bloodstream. These five examples cover the range.
1. Radiocarbon Dating
Cosmic rays make carbon-14 in the upper atmosphere, and living things absorb it at a steady rate. When an organism dies, intake stops and the carbon-14 beta-decays to nitrogen-14 with a half-life of 5,730 years.
Measure how much is left, count the half-lives, and you have an age. The method reaches back roughly 50,000 years before the remaining activity is too faint to measure.
2. The Radioactivity Inside You
Potassium-40 makes up about 0.012% of all natural potassium, and your body cannot tell it apart from ordinary potassium. An adult carries around 4,300 becquerels of it, and roughly nine in ten of those decays are beta-minus events producing calcium-40.
The rest proceed by electron capture to argon-40 — which is why nearly 1% of the air you breathe is argon that leaked out of decaying rock.
3. PET Scans
Fluorine-18 is bonded into a glucose-like molecule and injected. Tumours, which consume glucose greedily, concentrate it. The fluorine-18 beta-plus decays with a 110-minute half-life, and each positron annihilates within millimetres, firing two 511 keV photons in exactly opposite directions.
Detectors in a ring catch both, draw the line between them, and reconstruct where the decay happened. The image is built entirely from beta-plus decays.
4. Glow-in-the-Dark Exit Signs
The green emergency signs in aircraft and cinemas often contain tritium gas. Tritium beta-decays to helium-3 with a half-life of 12.3 years and an endpoint energy of just 18.6 keV — so feeble the electrons cannot penetrate the glass, but energetic enough to make a phosphor coating glow.
No battery, no wiring, roughly a decade of light. Beta decay as a power source.
5. Reactor Antineutrinos
Fission fragments are violently neutron-rich, so they beta-decay in long chains, and each step releases an antineutrino. A large power reactor emits something like 1021 of them per second.
Almost all pass straight through the Earth. This is the flux that Cowan and Reines used in 1956, and the same one that modern detectors monitor to verify reactor operation from outside the building.
| Isotope | Mode | Half-life | Decay energy Q | Daughter | Where you meet it |
|---|---|---|---|---|---|
| Carbon-14 | β− | 5,730 years | 156 keV | Nitrogen-14 | Radiocarbon dating |
| Tritium (H-3) | β− | 12.3 years | 18.6 keV | Helium-3 | Self-powered exit signs |
| Potassium-40 | β− (~89%) / EC (~11%) | 1.25 billion years | 1.311 MeV (β−) | Calcium-40 / Argon-40 | Your body; K-Ar rock dating |
| Strontium-90 | β− | 28.8 years | 546 keV | Yttrium-90 | Fallout; thickness gauges |
| Iodine-131 | β− | 8.02 days | 971 keV | Xenon-131 | Thyroid therapy |
| Fluorine-18 | β+ | 110 minutes | 634 keV | Oxygen-18 | PET imaging |
| Sodium-22 | β+ | 2.60 years | 1.821 MeV | Neon-22 | Laboratory positron source |
| Beryllium-7 | EC | 53.2 days | 862 keV | Lithium-7 | Solar and atmospheric studies |
Q is the total decay energy. Where the daughter is left excited, the beta particle takes only part of it and gamma photons carry away the rest.
Common Misconceptions About Beta Decay
“The electron was hiding in the nucleus”
It was not. Nuclei contain only protons and neutrons, and confining an electron to a space that small would demand far more energy than beta decay releases. The beta particle is created at the moment of decay, exactly as a photon is created when an atom emits light.
“Beta decay changes the mass number”
A is fixed. One nucleon changes identity, so the count of nucleons never moves — carbon-14 becomes nitrogen-14, not nitrogen-13. In the periodic table the nucleus steps sideways along the same mass row, unlike alpha decay, which drops A by four.
“All beta particles from one isotope have the same energy”
They do not, and this is the single most useful fact about beta decay. Energies form a continuous spectrum up to the endpoint, because the antineutrino takes an unpredictable share. When a table lists carbon-14 at 156 keV, that is the maximum, not the typical value.
“Beta radiation is harmless because it is only an electron”
Beta particles are stopped by a few millimetres of aluminium, so external exposure is far less penetrating than gamma radiation. Swallow or inhale a beta emitter, though, and that same short range becomes the danger — all the energy is dumped into a small volume of tissue. Strontium-90 is feared precisely because the body mistakes it for calcium and files it into bone.
How Beta Decay Relates to Half-Life, Alpha and Gamma Radiation
Beta decay is one of three classical decay modes, and it sits between alpha and gamma in both mechanism and penetrating power. Our full comparison of alpha, beta and gamma radiation puts all three side by side.
Alpha decay ejects an existing cluster of two protons and two neutrons, dropping A by 4 and Z by 2. Gamma emission changes neither — it is a nucleus shedding surplus energy as a photon, usually immediately after an alpha or beta event has left it excited.
That last point explains a common source of confusion. Cobalt-60 is used as a gamma source, yet cobalt-60 is a beta emitter; the beta decay produces an excited nickel-60 nucleus, and it is the nickel that releases the famous 1.17 and 1.33 MeV gammas.
Beta decay is also random per nucleus, so a population follows exponential decay. You cannot predict when one nucleus will go, but a large sample halves with clockwork reliability — see our guide to half-life and decay constants, or run the numbers directly in the Half-Life Calculator if you have a sample and want the age.
One useful pattern: the larger the Q-value, the faster the decay. Tritium releases only 18.6 keV and takes 12.3 years, while a fission fragment releasing several MeV can be gone in seconds.
Worked Problems
Show Solution
Solution:
Step 1: In β− decay, A stays the same and Z increases by 1.
Step 2: Carbon has Z = 6, so the parent is 146C. The daughter has Z = 7, which is nitrogen, and A = 14.
Step 3: Add the emitted electron and antineutrino to balance charge and lepton number.
146C → 147N + e− + ν̄e
Check: mass numbers 14 = 14 ✓. Charges 6 = 7 + (−1) ✓.
Answer: the daughter is nitrogen-14.
Show Solution
Solution:
Step 1: Q = [mn − mp − me]c2, using nuclear (not atomic) masses.
Step 2: Δm = 1.008665 − 1.007276 − 0.000549 = 0.000840 u
Step 3: Q = 0.000840 u × 931.494 MeV/c2 per u = 0.7825 MeV
Answer: Q = 0.782 MeV (782 keV).
Show Solution
Solution:
Step 1: For β− using atomic masses, Q = [M(C-14) − M(N-14)]c2. The electron masses cancel, so no correction term is needed.
Step 2: Δm = 14.003242 − 14.003074 = 0.000168 u
Step 3: Q = 0.000168 × 931.494 = 0.1565 MeV
Answer: Q = 156 keV, the maximum beta energy. Typical emitted electrons carry roughly 49 keV, the balance going to the antineutrino.
Show Solution
Solution:
Step 1: For β+, Q = [M(Na-22) − M(Ne-22) − 2me]c2. The 2me term is required because atomic masses are used.
Step 2: Δm = 21.994437 − 21.991385 = 0.003052 u → 0.003052 × 931.494 = 2.843 MeV
Step 3: Subtract 2mec2 = 1.022 MeV: Q = 2.843 − 1.022 = 1.821 MeV
Answer: Q = 1.82 MeV.
Show Solution
Solution:
Step 1: Beta-plus and electron capture connect the same two nuclides, but β+ must additionally create a positron and account for the lost orbital electron: Q(β+) = Q(EC) − 2mec2.
Step 2: 2mec2 = 2 × 0.511 = 1.022 MeV
Step 3: Q(β+) = 0.90 − 1.022 = −0.12 MeV. A negative Q means the decay is energetically forbidden.
Answer: No. Beta-plus is impossible below 1.022 MeV, so this nuclide decays by electron capture only.
Show Solution
Solution:
Step 1: Activity is proportional to the number of C-14 nuclei, so N/N0 = 0.25.
Step 2: 0.25 = (½)n, so n = 2 half-lives.
Step 3: t = 2 × 5,730 = 11,460 years
Answer: about 11,500 years old (11,460 years).
Show Solution
Solution:
Step 1: Number of nuclei: N = (1.0 × 10−6 g ÷ 90 g/mol) × 6.022 × 1023 /mol = 6.7 × 1015 nuclei
Step 2: Decay constant: λ = ln2 ÷ t½ = 0.6931 ÷ (28.8 × 3.156 × 107 s) = 7.63 × 10−10 s−1
Step 3: Activity: A = λN = 7.63 × 10−10 × 6.7 × 1015 = 5.1 × 106 Bq
Answer: A ≈ 5.1 MBq (about 5.1 million beta decays per second from one microgram).
