{"id":863,"date":"2026-08-21T14:53:09","date_gmt":"2026-08-21T14:53:09","guid":{"rendered":"https:\/\/physicsfundamentalsinfo.com\/blog\/?p=863"},"modified":"2026-08-24T13:03:36","modified_gmt":"2026-08-24T13:03:36","slug":"beta-decay","status":"publish","type":"post","link":"https:\/\/physicsfundamentalsinfo.com\/blog\/nuclear-physics\/beta-decay\/","title":{"rendered":"Beta Decay Explained"},"content":{"rendered":"\n
Definition<\/div>

\nBeta 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.\n<\/p><\/div>\n\n

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 \u2014 the overwhelming majority by beta decay.<\/p>\n\n

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.<\/p>\n\n

What Is Beta Decay?<\/h2>\n\n

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.<\/p>\n\n

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 \u2014 because they are sorted into the wrong columns.<\/p>\n\n

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.<\/p>\n\n

The Particle Everyone Gets Wrong<\/h3>\n\n

Here is the part that trips up almost every student. The emitted electron was never inside the nucleus.<\/p>\n\n

Nuclei contain protons and neutrons \u2014 no electrons. The beta particle is manufactured<\/em> 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.<\/p>\n\n

The Beta Decay Formula and Equations<\/h2>\n\n

The core equation is the decay of a single neutron, and every beta-minus event in every nucleus is a version of it:<\/p>\n\n

n \u2192 p + e\u2212<\/sup> + \u03bd\u0304e<\/sub><\/div>\n\n

Written for a whole nucleus, with X the parent and Y the daughter:<\/p>\n\n

A<\/sup>Z<\/sub>X \u2192 A<\/sup>Z+1<\/sub>Y + e\u2212<\/sup> + \u03bd\u0304e<\/sub><\/div>\n\n

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.<\/p>\n\n

\n\n\n\n\n
Symbol<\/th>\nQuantity<\/th>\nSI unit<\/th>\n<\/tr>\n<\/thead>\n
A<\/td>Mass number (protons + neutrons)<\/td>dimensionless<\/td><\/tr>\n
Z<\/td>Atomic number (proton count)<\/td>dimensionless<\/td><\/tr>\n
e\u2212<\/sup><\/td>Beta particle (electron), charge \u22121.602 \u00d7 10\u221219<\/sup> C<\/td>coulomb (C)<\/td><\/tr>\n
\u03bd\u0304e<\/sub><\/td>Electron antineutrino (neutral, near-zero mass)<\/td>\u2014<\/td><\/tr>\n
Q<\/td>Decay energy released, shared by the products<\/td>joule (J); usually quoted in MeV<\/td><\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n\n

Working Out the Decay Energy<\/h3>\n\n

The energy released is called the Q-value, and it comes straight from the mass difference between parent and daughter. Using atomic<\/strong> masses, the electron masses cancel automatically for beta-minus:<\/p>\n\n

Q = [M(A, Z) \u2212 M(A, Z+1)]c2<\/sup><\/div>\n\n

For beta-plus decay you must subtract two electron masses, because the parent atom sheds one orbital electron while the nucleus creates a positron:<\/p>\n\n

Q = [M(A, Z) \u2212 M(A, Z\u22121) \u2212 2me<\/sub>]c2<\/sup><\/div>\n\n

These are the standard relations used in evaluated nuclear data; the National Nuclear Data Center<\/a> publishes measured Q-values for every known nuclide on exactly this basis.<\/p>\n\n

Convert mass to energy with 1 u = 931.494 MeV\/c2<\/sup>. A convenient shortcut: 2me<\/sub>c2<\/sup> = 1.022 MeV, a number that turns out to decide whether beta-plus decay can happen at all. If mass-energy equivalence<\/a> is new to you, that conversion is the whole idea in one line.<\/p>\n\n

The Three Types of Beta Decay<\/h2>\n\n

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.<\/p>\n\n

Beta-Minus (\u03b2\u2212<\/sup>): Too Many Neutrons<\/h3>\n\n

A neutron converts to a proton, throwing out an electron and an electron antineutrino. This is the common case \u2014 most nuclei made in reactors and in stellar nucleosynthesis are neutron-rich, and beta-minus is how they climb back toward stability.<\/p>\n\n

Beta-Plus (\u03b2+<\/sup>): Too Many Protons<\/h3>\n\n

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<\/a>.<\/p>\n\n

Beta-plus has a hard energy threshold. The nucleus must supply the rest mass of the new positron and<\/em> pay back the orbital electron the atom loses \u2014 1.022 MeV in total. Below that, it simply cannot happen.<\/p>\n\n

Electron Capture: The Quiet Alternative<\/h3>\n\n

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.<\/p>\n\n

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.<\/p>\n\n

\n\n\n\n\n
Feature<\/th>\nBeta-minus (\u03b2\u2212<\/sup>)<\/th>\nBeta-plus (\u03b2+<\/sup>)<\/th>\nElectron capture<\/th>\n<\/tr>\n<\/thead>\n
Nucleon change<\/strong><\/td>n \u2192 p<\/td>p \u2192 n<\/td>p + e\u2212<\/sup> \u2192 n<\/td><\/tr>\n
Emitted particles<\/strong><\/td>Electron + antineutrino<\/td>Positron + neutrino<\/td>Neutrino only, then X-rays<\/td><\/tr>\n
Atomic number Z<\/strong><\/td>+1<\/td>\u22121<\/td>\u22121<\/td><\/tr>\n
Mass number A<\/strong><\/td>Unchanged<\/td>Unchanged<\/td>Unchanged<\/td><\/tr>\n
Triggered by<\/strong><\/td>Neutron excess<\/td>Proton excess<\/td>Proton excess<\/td><\/tr>\n
Energy threshold<\/strong><\/td>Any Q > 0<\/td>Needs 1.022 MeV<\/td>No 1.022 MeV threshold<\/td><\/tr>\n
Typical example<\/strong><\/td>Carbon-14<\/span><\/td>Fluorine-18<\/span><\/td>Beryllium-7<\/span><\/td><\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n\n

How Beta Decay Works Inside the Nucleus<\/h2>\n\n

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.<\/p>\n\n

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.<\/p>\n\n

In beta-minus decay, one down quark emits a W\u2212<\/sup> boson and becomes an up quark. The W\u2212<\/sup> is enormously heavy \u2014 about 80 GeV\/c2<\/sup>, some 85 times the mass of the whole neutron \u2014 so it can exist only for the fleeting interval quantum mechanics allows, then immediately splits into the electron and the antineutrino we detect.<\/p>\n\n

How long a free neutron actually lasts is still an open question. Two techniques \u2014 counting surviving neutrons in a bottle, and counting the protons produced in a beam \u2014 disagree by about nine seconds, far more than their stated uncertainties, and NIST notes the discrepancy is not yet understood<\/a>.<\/p>\n\n

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.<\/p>\n\n

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\u221222<\/sup> seconds. Curious about the quarks themselves? Our guide to quarks and the Standard Model<\/a> unpacks the full particle family.<\/p>\n\n

\"Beta<\/figure>
Beta decay at the quark level: a down quark emits a W boson, becomes an up quark, and the neutron is now a proton.<\/figcaption><\/figure>\n\n
<\/span>Beta Decay Lab<\/span><\/div>