Alpha, Beta and Gamma Decay: What Changes in the Nucleus
Alpha, Beta and Gamma Decay: What Changes in the Nucleus
Type the parent and the daughter and the page names the decay — and tells you the one case where Z and A cannot name it, because beta-plus decay and electron capture leave the nucleus in exactly the same place.
Identify the decay from the parent and the daughter
Uranium-238 decaying to thorium-234: Z from 92 to 90, A from 238 to 234
Two conservation rules, and four numbers that are not always enough
- ΔA
- the change in mass number. Only four values occur in ordinary decay: −4 for alpha, −1 for single nucleon emission, −2 for two-nucleon emission, and 0 for every beta and gamma process. A decay NEVER increases A
- ΔZ
- the change in proton number, and the thing that decides whether the element changes. Gamma emission alone leaves it untouched, which is why a gamma emitter is still the same element afterwards — technetium-99m decays to technetium-99 and not to anything else
- β⁻
- a neutron becomes a proton, so Z goes UP although a negative particle came out. This looks backwards and is the reason beta-minus is the decay students get wrong most often. The electron was created in the decay; it was not a constituent of the nucleus beforehand
- β⁺ against EC
- identical in Z and A, and therefore not distinguishable by these four numbers at all. Energetics separates them: beta-plus decay must create a positron and needs at least 1.022 MeV of mass difference between the parent and daughter ATOMS — two electron rest masses — while electron capture has no threshold. Below 1.022 MeV only capture is open
- the neutrino
- carries no charge and no nucleons, so it is invisible to both conservation rules on this page and must still be written in the equation. Its existence was inferred precisely BECAUSE beta particles come out with a continuous spread of energies instead of the single value these two rules alone would predict
Worked example
Uranium-238 decaying to thorium-234: Z from 92 to 90, A from 238 to 234
BALANCE THE MASS NUMBERS. 238 on the left, 234 on the right, so whatever left took four nucleons with it: Aemitted = 4.
BALANCE THE PROTON NUMBERS. 92 on the left, 90 on the right, so the emitted thing carried two units of positive charge: Zemitted = 2.
IDENTIFY IT. Four nucleons of which two are protons is a helium-4 nucleus: two protons and two neutrons. That is an alpha particle, and the decay is written 23892U → 23490Th + 42He.
WHY A CLUMP OF FOUR, which is the question behind the rule. Because helium-4 is anomalously tightly bound: 7.0739 MeV per nucleon against 5.3323 for lithium-6 and 5.6064 for lithium-7, as the binding energy per nucleon page shows. Emitting those four nucleons already bound together takes 28.3 MeV of binding energy out of the problem, which is what makes the decay energetically possible when emitting them one at a time would not be.
WHAT HAPPENS NEXT, because this is the first step of a chain and not the end of it. Thorium-234 beta-minus decays to protactinium-234 (ΔZ = +1), which beta-decays again to uranium-234, which alpha-decays, and so on through fourteen steps to lead-206. If a question hands you uranium-238 and lead-206 as parent and daughter, the numbers differ by 32 in A and 10 in Z — which is eight alphas (−32 in A, −16 in Z) plus six beta-minus decays (+6 in Z) — and no single decay will match it.
AND THE RATE, which these numbers say nothing about. Conservation of A and Z tells you WHAT happens and gives no information at all about WHEN. Uranium-238's half-life is 4.5 billion years and polonium-214's is 164 microseconds, and both are alpha decays with exactly the same ΔA and ΔZ. For the timing, the arithmetic is on the half-life and decay constant page and the radioactive decay and activity page.
Every change a single decay can make to Z and A
| Decay | ΔA | ΔZ | What is emitted | How common |
|---|---|---|---|---|
| alpha | −4 | −2 | a helium-4 nucleus | the dominant mode above lead |
| beta-minus | 0 | +1 | an electron and an antineutrino | the dominant mode for neutron-rich nuclides |
| beta-plus | 0 | −1 | a positron and a neutrino | proton-rich nuclides, above a 1.022 MeV threshold |
| electron capture | 0 | −1 | a neutrino only — an inner atomic electron is absorbed | proton-rich nuclides, no threshold; favoured in heavy elements |
| gamma / isomeric transition | 0 | 0 | a photon | follows most other decays; the only mode that changes nothing but energy |
| internal conversion | 0 | 0 | an atomic electron, in place of a photon | competes with gamma emission, more so in heavy elements |
| neutron emission | −1 | 0 | a neutron | rare as a ground-state mode; common promptly after fission |
| proton emission | −1 | −1 | a proton | rare; proton-rich nuclides only |
| two-neutron emission | −2 | 0 | two neutrons | very rare, radioactive beam facilities |
| two-proton emission | −2 | −2 | two protons | very rare |
| double beta-minus | 0 | +2 | two electrons and two antineutrinos | about a dozen nuclides, half-lives beyond 10¹⁹ years |
| carbon-14 cluster decay | −14 | −6 | an intact carbon-14 nucleus | radium-223, about one decay in 10⁹ |
| spontaneous fission | large and negative | large and negative | two big fragments and a few neutrons | californium-252, about 3 per cent of its decays |
The three classic decays, drawn on the chart of nuclides
| Decay | Where it moves the nuclide | Why it goes that way |
|---|---|---|
| alpha | two steps left and two steps down — Z and N both fall by two | heavy nuclides have too many nucleons for the nuclear force to hold against Coulomb repulsion, so they shed four at a time in the most tightly bound package available |
| beta-minus | one step right and one step up the Z axis — N falls by one, Z rises by one | the nuclide has too many neutrons for its Z, and converting one into a proton moves it towards the line of stability |
| beta-plus or electron capture | one step left — Z falls by one, N rises by one | the nuclide has too few neutrons for its Z, and the same conversion runs the other way |
| gamma | nowhere at all | the nuclide is already the right one; it is simply holding energy it has not yet released |
Two conservation rules name the decay — except once, and that exception is the point
Balance the two numbers and the decay names itself. Mass number must balance and proton number must balance. A fall of four in A and two in Z is an alpha particle, because that is a helium-4 nucleus. A fall of one in A with no change in Z is a neutron. No change in A with a rise of one in Z is beta-minus, because a neutron inside the nucleus turned into a proton. No change in either is a gamma ray. Four of the five modes a syllabus asks about are read straight off the arithmetic.
The exception is worth more than the rule. No change in A with a fall of one in Z can be two entirely different processes. Beta-plus decay: a proton becomes a neutron, a positron and a neutrino leave. Electron capture: the nucleus swallows one of its own inner atomic electrons, a proton becomes a neutron, and only a neutrino leaves. The nuclear bookkeeping is identical, so a question that gives you Z and A alone cannot distinguish them and a mark scheme that insists on one answer is asking you to guess. What actually separates them is energy. A positron has to be CREATED, and creating one while also having lost an electron from the daughter’s atomic shell costs two electron rest masses, 1.022 MeV, of mass difference between parent and daughter atoms. Below that threshold beta-plus decay is impossible and electron capture is the only route open, which is why capture dominates among heavy nuclides where the inner electrons are closest to the nucleus.
Where this goes wrong. Three places, and the first is almost universal. Beta-minus emits a negative particle and Z goes UP. It feels wrong and it is right: a neutron became a proton, and the electron was created in the decay rather than having been in the nucleus to start with. Second, gamma emission changes neither Z nor A, so a gamma emitter is still the same element afterwards — technetium-99m becomes technetium-99 and nothing else. Third, a question that gives you the two ENDS of a decay chain and asks for “the decay”: uranium-238 to lead-206 is ΔA = −32 and ΔZ = −10, which is eight alpha decays and six beta-minus decays, and no single process does it. This page says so rather than guessing.
And what these numbers cannot tell you. Nothing about the rate. Uranium-238 and polonium-214 are both alpha emitters with the same ΔA = −4 and ΔZ = −2, and half-lives of 4.5 billion years and 164 microseconds. For the rate, λ = ln2/t½ is on the half-life and decay constant page; how an activity falls over a stated interval is on the radioactive decay and activity page; how many becquerels a given mass of a nuclide gives is on the specific activity and source mass page; and if what you actually have is an assayed source with a calibration date, the correction is on the decay correction page. The energetics — how much is released and whether the decay is possible at all — come from the mass difference, which is the binding energy per nucleon calculation.
Frequently asked questions
In beta-minus decay, why does the proton number increase when a negative particle is emitted?
Because a neutron inside the nucleus turned into a proton. The electron that comes out was CREATED in that conversion — it was not a constituent of the nucleus beforehand — and it carries the negative charge away so that charge is conserved: a neutral neutron becomes a positive proton plus a negative electron. The mass number is unchanged because the total nucleon count is unchanged; one of them has simply changed type. This is the single most commonly misremembered fact in the whole topic, and the way to hold on to it is to think about what happened to the NUCLEON rather than about the sign of the particle that left.
How do I tell beta-plus decay from electron capture?
Not from Z and A, because they are identical in both: A unchanged, Z down by one. You need the energetics. Beta-plus decay creates a positron, and between the positron’s rest mass and the electron the daughter atom no longer needs, it requires at least 1.022 MeV of mass difference between the parent and daughter neutral atoms. Electron capture has no such threshold because nothing has to be created — an existing atomic electron is absorbed. So below 1.022 MeV only capture is possible; above it both compete, and capture is increasingly favoured in heavy elements because their inner electrons spend more time close to the nucleus. If a question gives you only the two nuclides, the honest answer names both.
Does gamma emission change the element?
No. Gamma emission changes neither Z nor A, so the nuclide afterwards is the same nuclide, in a lower energy state. Technetium-99m becomes technetium-99; cobalt-60 emits its gammas as part of a beta-minus decay to nickel-60, and it is the beta step that changes the element, not the gammas. The same ΔA = 0, ΔZ = 0 arithmetic covers internal conversion, where the energy ejects an atomic electron instead of making a photon, and an isomeric transition from a long-lived excited state.
Why is it a helium-4 nucleus that is emitted and not some other clump?
Because helium-4 is anomalously tightly bound. Its binding energy per nucleon is 7.0739 MeV, well above both lithium-6 at 5.3323 and lithium-7 at 5.6064, so the four nucleons arrive on the other side already holding 28.3 MeV of binding energy that no longer has to be paid for. That surplus is what makes the decay energetically possible when emitting a lone proton or neutron would not be. The same logic explains the rare cluster decays: carbon-14 and neon-24 are also local peaks on the binding curve, and those are exactly the clusters that get emitted.
Do these four numbers tell me anything about the half-life?
Nothing at all. Uranium-238 and polonium-214 are both alpha emitters with identical ΔA and ΔZ, and their half-lives are 4.5×109 years and 164 microseconds — a factor of 1021. What changes the rate is the energy released and the height and width of the barrier the emitted particle has to tunnel through, and a small change in decay energy produces an enormous change in half-life. Conservation of A and Z tells you what is emitted; it says nothing about when. For the rate, see the half-life and decay constant calculator.
Related calculators
References
- W. J. Huang, M. Wang, F. G. Kondev, G. Audi and S. Naimi, “The AME 2020 atomic mass evaluation”, Chinese Physics C 45 (2021) 030002 and 030003. The mass table, read from www-nds.iaea.org/amdc/ame2020/AME2020-b.pdf on 11 November 2026. Every light nuclide on this page carries its AME2020 atomic mass to eleven figures — 4He is 4.002 603 254 13 u, 12C is 12 exactly by definition, 14C is 14.003 241 989 u. The copy of the table that could be read for this build stops at about A = 51, so the iron-peak nuclides here are NIST relative atomic masses instead, and that is said on the page rather than hidden. The AME’s own printed binding energies per nucleon were used as a check: recomputing them from the masses with B = Z·m(1H) + N·m(n) − M reproduced all fifteen to within 1 eV per nucleon, which is what licenses the same method on the NIST masses.
- CODATA Internationally Recommended 2022 Values of the Fundamental Physical Constants, NIST Standard Reference Database 121, read 11 November 2026 from the machine-readable table at physics.nist.gov/cuu/Constants/Table/allascii.txt. The table prints the word (exact) against the Planck constant, the speed of light in vacuum and the elementary charge, which is the single most consequential thing on it for a student: h = 6.626 070 15×10−34 J Hz−1, c = 299 792 458 m/s and e = 1.602 176 634×10−19 C have no uncertainty to quote because the 2019 revision of the SI defines the kilogram, the metre and the ampere through them. The electron mass, 9.109 383 7139(28)×10−31 kg, is still measured and still carries an uncertainty; so does the atomic mass constant, 931.494 103 72(29) MeV.
- F. G. Kondev, M. Wang, W. J. Huang, S. Naimi and G. Audi, “The NUBASE2020 evaluation of nuclear physics properties”, Chinese Physics C 45 (2021) 030001. The companion evaluation to the mass table, and the reference work that records which decay modes each nuclide actually has and in what branching ratios. Cited for the existence and rarity of the exotic modes rather than for a branching ratio: the percentages quoted here — about three per cent spontaneous fission for californium-252, about one in 109 carbon-14 cluster decay for radium-223 — could not be confirmed against NUBASE2020 in this build, so they are given as orders of magnitude and not as evaluated values.
- NCERT, Physics, Textbook for Class XII, Part II — the chapter on the dual nature of radiation and matter, which is where the work-function table most Indian students are working from is printed. This could not be read for this page. The official PDF at ncert.nic.in is served under a robots policy that refuses automated retrieval, and every copy a search returns is a coaching-site mirror with no provenance. So no number on this page is attributed to NCERT, and where this page and a school table differ the difference is stated against sources that could be read. That is a weaker claim than “the textbook is wrong” and it is deliberately the weaker one.