In short
An unstable nucleus spontaneously emits a particle or a photon and transforms into a different (generally more stable) nucleus. The three principal emissions are called, in historical order, alpha, beta, and gamma rays. In modern language:
Alpha decay — emission of a ^4_2\text{He} nucleus (two protons + two neutrons):
Common in heavy nuclei (A > 200, e.g. uranium, thorium, radium). Reduces Z by 2 and A by 4.
Beta-minus decay — a neutron inside the nucleus becomes a proton, emitting an electron and an electron antineutrino:
Common in neutron-rich nuclei. Z increases by 1, A unchanged.
Beta-plus decay — a proton becomes a neutron, emitting a positron and an electron neutrino:
Common in proton-rich nuclei. Z decreases by 1, A unchanged.
Gamma decay — emission of a high-energy photon from a nucleus in an excited state:
Neither Z nor A changes; the nucleus simply releases energy as a photon. Typical gamma energies are 0.1 to 10 MeV — ten thousand times more energetic than visible-light photons.
In every decay: nucleon number A (total), charge Z (total), energy, momentum, and angular momentum are all conserved. The neutrino was postulated in 1930 by Pauli specifically to save these conservation laws in beta decay — it was then invisible for 26 years, until Reines and Cowan detected it directly in 1956, and India's own contribution came in the mid-1960s when the Kolar Gold Fields experiment (conducted 2300 m underground by TIFR, BARC, and Osaka City University) detected the first atmospheric-neutrino events ever recorded.
Put a speck of uranium salt on a photographic plate and wrap the plate in light-tight paper. Leave it in a drawer for a few days. Develop the plate. There will be a dark spot where the salt was, as though the plate had been exposed to light — even though the paper blocked every photon that hit the outside. This is the 1896 experiment of Henri Becquerel, and it was the accidental discovery of radioactivity. Something was coming out of the uranium, passing through black paper, and exposing silver bromide grains on the other side. Whatever it was, it came out at a steady rate, could not be stopped by chemistry, was not affected by heat or cold, and did not care whether the uranium was locked in a crystal of uranyl sulphate or dissolved in water. It was coming from inside the atom, from a part of the atom that chemistry could not reach.
Within a few years, Rutherford had separated what was coming out into three components by deflecting them through a magnetic field. The first, deflected a little in one direction, turned out to be a heavy positive particle — he called it an alpha ray, identified it as a ^4He nucleus by 1908. The second, deflected a lot in the opposite direction, was a light negative particle — a beta ray, soon identified as an electron. The third passed straight through the magnetic field without deflecting — a neutral gamma ray, a photon of very short wavelength. Alpha, beta, gamma, in decreasing order of ionising power and increasing order of penetration.
A century of nuclear physics has since broken each of these into a finer classification and added one that Rutherford missed (positron emission, discovered in 1934 by Joliot-Curie). But the big picture is the same as in 1898: an unstable nucleus loses energy by emitting a particle, and the particle it emits is dictated by which conservation laws get satisfied in the cheapest way. This article derives what those particles are and why, for each of the four principal decay modes.
What makes a nucleus unstable
Look at the chart of all known nuclei — the Segrè chart — plotted with neutron number N horizontal and proton number Z vertical. A small zig-zag band of stable nuclei runs roughly along the line N = Z for light nuclei and curves up to N \approx 1.5\,Z for heavy nuclei (the curvature is the Coulomb-repulsion fingerprint from the semi-empirical mass formula). Out of the roughly 3300 known nuclides, only 253 are genuinely stable. All the rest are radioactive.
Which decay mode a given unstable nucleus chooses depends on where it sits relative to this band. The driver is always the same — the nucleus wants to increase its binding energy per nucleon and move toward the peak at iron — but the route depends on the geometry.
Alpha decay — shedding a helium nucleus
A nucleus that is too heavy (more than about A = 200 nucleons) can lower its energy by ejecting a tightly-bound cluster of two protons plus two neutrons — a ^4_2\text{He} nucleus, the alpha particle. The alpha particle is the most tightly bound few-nucleon cluster available: its binding energy is 28.3 MeV, which is 7.1 MeV per nucleon, far above the binding energy of a free deuteron or triton. When a heavy nucleus releases an alpha, it hands off 28.3 MeV of internal binding to the alpha as external kinetic energy — plus it reduces its own Coulomb energy because it now has fewer protons. For nuclei above uranium, the arithmetic favours alpha decay decisively.
The general equation:
Conservation bookkeeping. On the left: nucleon number A, proton number Z. On the right: nucleon number (A-4) + 4 = A ✓, proton number (Z-2) + 2 = Z ✓. Both balances hold automatically.
Energy release (Q-value). The energy released in the decay is the difference between the initial and final nuclear masses times c^2:
This energy comes out as kinetic energy of the alpha (and a small recoil of the daughter nucleus).
Why alphas come out with specific energies. Unlike beta decay (below), alpha decay is a two-body process: parent → daughter + alpha. By conservation of momentum (the parent is at rest), the alpha and the daughter fly apart with equal and opposite momenta. Combined with conservation of energy, this fixes both momenta uniquely. So alpha particles from a particular decay come out monoenergetic — all ^{238}\text{U} alphas emerge at 4.267 MeV; all ^{226}\text{Ra} alphas at 4.784 MeV. A pulse-height spectrum of alpha particles from a radioactive sample shows sharp, distinct lines. (In fact there are often a few lines per decay — corresponding to the daughter ending up in the ground state vs. various excited states — but each line is sharp.)
Canonical example — the first step of the uranium-238 decay chain.
The alpha carries away most of the energy (it has much smaller mass than the daughter; momentum conservation gives it the lion's share of the kinetic energy). The thorium-234 daughter is itself radioactive and decays further — by beta-minus, in the next section — to ^{234}Pa, and so on through a chain of 14 decays before arriving at stable ^{206}Pb. This is the uranium-238 decay series, and it is what makes every granite countertop very slightly radioactive.
Why not emit a single proton or a deuteron? An alpha is the winning configuration because ^4He is doubly magic (Z = N = 2) and extremely tightly bound. Emitting a single proton or a neutron requires first unbinding it from the nucleus (costing \sim 5–8 MeV), and then providing its kinetic energy. Unless Q_p or Q_n happens to be positive (it almost never is, for naturally occurring heavy isotopes), the decay is energetically forbidden. Emitting a ^3He or a ^3H is similarly expensive because these are less tightly bound than ^4He. The alpha is the cheapest exit ticket, and that is why — empirically — it is the only large cluster commonly emitted from heavy nuclei (very rare "cluster decay" modes emitting ^{12}C or ^{14}C are known but have half-lives 10 billion times longer than the competing alpha channel).
Beta-minus decay — a neutron becomes a proton
A nucleus with too many neutrons relative to protons (below the stability band) transforms a neutron into a proton, emitting an electron and an antineutrino to conserve charge, energy, and lepton number:
At the fundamental level, this is a process involving a single neutron inside the nucleus:
This is precisely the same decay that a free neutron undergoes with a 10.2-minute half-life. Inside many nuclei, the process is forbidden because the final proton state is already occupied (Pauli exclusion), but in neutron-rich nuclei a free proton slot is available and the decay proceeds.
Conservation bookkeeping. Nucleon number: A = A + 0 + 0 ✓ (the electron and the antineutrino are not nucleons). Charge: Z e = (Z+1) e + (-e) + 0 ✓. Lepton number: 0 = 0 + 1 + (-1) ✓ (the electron is a lepton, L = +1; the electron antineutrino is an antilepton, L = -1).
Canonical example — carbon-14 dating.
Atmospheric ^{14}C is produced continuously by cosmic-ray neutrons hitting nitrogen in the upper atmosphere, and it beta-decays back to ^{14}N with a 5730-year half-life. Living organisms exchange carbon with the atmosphere and maintain a steady-state ^{14}C/^{12}C ratio of about 1.3 \times 10^{-12}. When an organism dies, the exchange stops and the ^{14}C decays away. Measure the ratio in a sample of ancient wood, charcoal, or bone, and you get the age — up to about 50,000 years before present, beyond which the remaining ^{14}C is too little to detect. The Physical Research Laboratory (PRL) in Ahmedabad runs an accelerator mass spectrometer for ^{14}C dating that has been used on samples from Harappan sites at Dholavira and at the prehistoric cave paintings in the Bhimbetka rock shelters. The physics that makes this possible is the beta-minus decay of a single neutron in a carbon-14 nucleus.
Why beta particles come out with a continuous spectrum. Here is the crucial observation that took thirty years to understand. If beta decay were a two-body process — parent → daughter + electron — then by the same two-body momentum argument as in alpha decay, the electron would come out monoenergetic. But measurements of beta spectra showed a continuous distribution, from zero up to some maximum energy E_\text{max} = Q. Electrons emerge with all energies in between.
The only way to reconcile a continuous spectrum with conservation of energy and momentum is to have a three-body decay, with the third body invisible. The missing particle (massless or very light, no charge) would carry away variable amounts of the total energy, letting the electron share with it in a continuous range.
Pauli's 1930 rescue. Wolfgang Pauli, in a famous 1930 letter to a nuclear physics conference in Tübingen that he could not attend, wrote: "I have hit upon a desperate remedy to save... the law of conservation of energy. Namely, the possibility that in the [nuclei] there could exist electrically neutral particles..., which have spin 1/2 and obey the exclusion principle..." He called them neutrons. Chadwick then actually discovered what we now call neutrons in 1932, and Pauli's invisible particle was renamed by Enrico Fermi the neutrino ("little neutral one" in Italian).
Fermi worked out the full quantum theory of beta decay in 1933 — a four-fermion contact interaction that was the first example of what we now call the weak nuclear force. His theory predicted the shape of the beta spectrum (a specific distribution called the Fermi function times the square of the neutrino energy), and it matched measurements beautifully. The neutrino had been forced into existence by a shape on a graph.
When was the neutrino finally seen? In 1956, Clyde Cowan and Frederick Reines detected antineutrinos from the Savannah River reactor in South Carolina by looking for the inverse reaction \bar\nu_e + p \to n + e^+ in a large tank of cadmium-doped water. The detection came 26 years after Pauli's letter. The Nobel Prize finally came in 1995 — Reines received it; Cowan had died in 1974. India's contribution: from 1965 onwards, the Kolar Gold Fields experiment (TIFR-BARC-Osaka collaboration), conducted 2.3 km underground in a working gold mine to shield from cosmic rays, detected the first atmospheric neutrinos — cosmic-ray-produced neutrinos passing through the Earth from the far side. KGF led directly to the contemporary proposal for the India-based Neutrino Observatory (INO) at Theni in Tamil Nadu. The ghostly particle Pauli postulated to save beta decay turned out to be the most abundant matter particle in the universe — a hundred billion neutrinos pass through your palm every second, most of them from the Sun.
Beta-plus decay — a proton becomes a neutron
A nucleus with too many protons (above the stability band) transforms a proton into a neutron, emitting a positron and an electron neutrino:
At the quark level: p \to n + e^+ + \nu_e — the mirror of beta-minus. Unlike free-neutron decay, free proton decay is not observed: a proton in vacuum is stable (or at least has a lifetime longer than 10^{34} years, and possibly infinite). Beta-plus only happens for a proton bound inside a nucleus, where the surrounding nuclear energy landscape can supply the energy needed to produce the final state.
Conservation bookkeeping. Charge: Z e = (Z-1)e + e + 0 ✓. Lepton number: 0 = 0 + (-1) + (+1) ✓ (positron is an antilepton L = -1; electron neutrino is a lepton L = +1).
Canonical example — fluorine-18 for PET imaging.
Fluorine-18 is produced in a cyclotron, bonded chemically to a glucose analogue (18F-fluorodeoxyglucose, or 18F-FDG), injected into a patient, and concentrated in metabolically active tissue (cancer cells, in particular, consume glucose at elevated rates). The ^{18}F nuclei beta-plus decay. Each positron travels a few millimetres through tissue before annihilating with a nearby electron, producing two 511 keV gamma photons flying off back-to-back. Ring detectors surrounding the patient record these coincident pairs and reconstruct the positron emission locations — positron emission tomography (PET). Every major cancer hospital in India (Tata Memorial Centre, AIIMS Delhi, Apollo) runs PET-CT scanners using fluorine-18 produced at on-site cyclotrons.
Energy threshold for beta-plus. Beta-plus decay produces a positron of mass m_e c^2 = 0.511 MeV. Energy conservation requires
where the factor of 2 m_e comes from accounting for the positron created and for the fact that atomic mass tables include Z electron masses: the parent has Z electrons, the daughter Z-1, and the positron emitted is an extra anti-electron. If Q_{\beta^+} would be negative — i.e., if the mass difference between neutral parent and daughter atoms is less than 2 m_e \cdot c^2 = 1.022 MeV — then beta-plus is forbidden, and the nucleus decays instead by electron capture, an alternative process where a bound K-shell electron is absorbed by a proton:
Electron capture looks like beta-plus in the nuclear balance (same Z shift, same A, same neutrino emitted) but produces no positron — just a neutrino and a hole in the K shell, which is then filled by an outer electron with emission of a characteristic X-ray (see the X-rays article). Electron capture and beta-plus can compete in nuclei where Q_{\beta^+} is small or negative.
Gamma decay — a nucleus drops to a lower level
The first three decay modes all change the identity of the nucleus (alpha changes both Z and A; beta changes Z alone). Gamma decay changes neither. It is the nuclear analogue of an atomic electron dropping from an excited orbital to a lower one — except the energy levels involved are those of the whole nucleus, and the energy scale is MeV instead of eV.
The asterisk denotes the excited state. After an alpha or beta decay, the daughter nucleus is often left in an excited nuclear state (it has not yet settled to the ground state because the emission of the particle could leave internal energy behind). The excited state then emits a gamma photon to reach the ground state.
Typical gamma energies. From about 0.05 MeV (50 keV) for low-lying transitions up to about 10 MeV for transitions in the lightest nuclei. A few well-known examples:
- ^{60}Co decay: the ^{60}Ni daughter after a beta-minus decay emits two gammas at 1.17 MeV and 1.33 MeV in cascade. This cobalt-60 is the standard high-energy gamma source used in teletherapy units at Tata Memorial Centre and the Cancer Institute, Chennai, for treating deep-seated tumours.
- ^{99m}Tc: a nuclear isomer (metastable state of technetium-99) that emits a single 140 keV gamma with a 6-hour half-life. This is the workhorse of nuclear medicine — bone scans, cardiac scans, thyroid imaging — used millions of times a year in India. The BRIT (Board of Radiation and Isotope Technology) facility at BARC produces ^{99m}Tc generators distributed nationwide.
- ^{14}N cosmic-ray reaction: when a cosmic-ray neutron is captured by ^{14}N, the resulting ^{15}N^* emits a 10.83 MeV gamma — close to the highest practical gamma energy in a decay spectrum.
Multipolarity and selection rules. Nuclear gamma transitions follow angular-momentum selection rules similar to atomic ones. The gamma photon carries intrinsic spin 1 and can also carry orbital angular momentum, so a transition of multipolarity \ell changes nuclear angular momentum by |\Delta J| = \ell (with parity change depending on whether it is an electric or magnetic multipole). Transitions with the smallest allowed \ell are fastest; higher multipoles are slower and tend to have observable lifetimes (hence the isomeric states that live long enough to be used clinically — ^{99m}Tc's 6-hour half-life is because its transition to the ground state requires a high-multipole change).
Internal conversion. Sometimes, instead of emitting a gamma, an excited nucleus dumps its energy directly into a bound atomic electron, ejecting it from the K or L shell. This is internal conversion, and it competes with gamma emission. The ejected electron has a sharp energy equal to the nuclear transition energy minus the electron's binding energy, and it leaves behind a vacancy that generates characteristic X-rays. Internal conversion is favoured for low-energy nuclear transitions in heavy atoms.
Decay diagram — alpha, beta-minus, beta-plus, gamma at a glance
Explore the decay mode — drag the parent nucleus on an N-Z grid
Worked examples
Example 1: Thorium-232 alpha decay — balance the equation and compute $Q$
^{232}Th is the starting nucleus of the thorium-232 decay series. It alpha-decays to an isotope of radium. Write the balanced nuclear equation and compute the released energy Q, given atomic masses M(^{232}\text{Th}) = 232.03806 u, M(^{228}\text{Ra}) = 228.03106 u, and M(^4\text{He}) = 4.00260 u. (1 u = 931.5 MeV/c².)
Step 1. Balance the nucleon and proton numbers.
Alpha decay reduces A by 4 and Z by 2:
Why: A: 232 \to 228 matches 228 + 4 = 232 ✓. Z: 90 \to 88 matches 88 + 2 = 90 ✓. The daughter has Z = 88, which is radium, so Y = \text{Ra}.
Step 2. Compute the mass difference.
Why: if the products weigh less than the parent, the missing mass has been converted to kinetic energy. This is the mass defect in action for a decay instead of for binding. When using atomic masses (which include all electrons), the electron count balances automatically — Th has 90 electrons, Ra has 88, He has 2, total 90 on both sides — so you can ignore the electrons.
Step 3. Convert to energy using 1\text{ u} = 931.5 MeV/c^2.
Why: Einstein's mass-energy relation. A mass difference of a few milli-atomic-mass-units translates to an energy release of a few MeV — the characteristic scale of alpha-decay energies.
Step 4. How does the energy split between the alpha and the recoiling ^{228}Ra? Two-body decay from rest, so momentum conservation gives p_\alpha = p_\text{Ra}, hence:
So E_\alpha = 57 E_\text{Ra} and E_\alpha + E_\text{Ra} = Q, giving:
Why: the alpha takes almost all (about 98%) of the released kinetic energy because it is so much lighter than the daughter. The daughter's recoil is small but not zero — important when you are trying to predict how an alpha-emitting thin film will move around.
Result. ^{232}_{\;90}\text{Th} \to ^{228}_{\;88}\text{Ra} + ^4_2\alpha, Q = 4.10 MeV, E_\alpha = 4.03 MeV.
What this shows. The alpha-decay half-life of ^{232}Th is 1.4\times 10^{10} years — about the age of the universe. A kilogram of natural thorium contains about 2.6\times 10^{24} ^{232}Th nuclei, and decays at a rate of roughly 4\times 10^6 per second (a few million alpha particles per second per kilogram). India has the world's largest reserves of thorium (in the monazite sands of the Kerala beaches), and the 3-stage nuclear programme planned by Homi Bhabha places thorium-based reactors at its culmination — running on the long-lived energy hidden in exactly this alpha-decay chain.
Example 2: Carbon-14 dating — how old is a piece of charcoal?
A 1-gram sample of charcoal from a Harappan archaeological site at Dholavira in Gujarat shows a ^{14}C activity of 9.8 decays per minute. Living carbon (from the current atmosphere) shows 15.3 decays per minute per gram. Assuming the sample's initial activity was the same as living carbon, how old is the sample? Given: half-life of ^{14}C is 5730 years.
Step 1. Write the beta-minus decay and confirm the daughter.
Why: beta-minus increases Z by one, leaves A unchanged. The daughter at Z = 7 is nitrogen. ^{14}N is the common stable isotope of nitrogen, which is why ^{14}C decays at all — its daughter is the abundant atmospheric nitrogen that originally produced it by cosmic-ray spallation.
Step 2. Write the decay law. The number of undecayed ^{14}C nuclei (and hence the activity A = \lambda N) falls exponentially:
Why: the derivation is in the radioactive decay law article. The half-life form A = A_0 \cdot 2^{-t/t_{1/2}} is most convenient for computing ages in terms of half-lives.
Step 3. Solve for t. Take the activity ratio:
Take the logarithm of both sides (use natural log, or log-base-2 — both work):
Why: \ln 0.6405 = -0.4455 (you can check: e^{-0.4455} \approx 0.6405). Divide by \ln 2 \approx 0.6931 to convert from natural-log to base-2-log. The answer comes out in the same units as t_{1/2} (years).
Step 4. Round appropriately. The activity measurements have maybe two significant figures, so report:
Result. The charcoal is about 3700 years old, placing it around 1700 BCE — the late Harappan period.
What this shows. Radiocarbon dating is a direct application of a single nucleus's half-life to archaeological timescales. The PRL Ahmedabad and IIT Bombay radiocarbon laboratories have dated hundreds of samples from sites across India — Mehrgarh, Mohenjo-daro, Dholavira, Lothal, Kalibangan — and the chronology they produced is the backbone of the accepted timeline of the Indus Valley civilisation. A single beta-minus decay rate, a single half-life, and every archaeological date back to 50,000 BCE becomes measurable.
Common confusions
- "Radioactivity is caused by chemistry or heat." No — radioactive decay rates are almost entirely unaffected by temperature, pressure, chemical environment, or magnetic fields. The decay is happening deep inside the nucleus, on energy scales of MeV, while chemistry operates on energy scales of eV (a million times smaller). The sole exception is electron capture, which depends on the electron density at the nucleus and can be affected by orders of magnitude of 10^{-3} by chemical bonding — measurable but tiny.
- "A beta particle is always an electron." It is the electron in beta-minus and the positron in beta-plus. Both are called beta particles, but they are different particles (one is the antiparticle of the other). Some nuclear physicists use \beta^- and \beta^+ exclusively to avoid confusion; for JEE, just remember: "beta minus" = electron, "beta plus" = positron.
- "Gamma rays are always the most penetrating." Usually yes. Alpha particles are stopped by paper or a few centimetres of air. Beta particles are stopped by a few millimetres of aluminium. Gamma rays can pass through centimetres of lead before being significantly attenuated. The ordering is because alpha particles lose energy quickly to many small ionisation events (short range), beta particles lose energy more slowly (longer range), and gamma photons interact only probabilistically via photoelectric, Compton, or pair-production processes (long mean free path).
- "Radioactive decay violates conservation of mass." It seems to, because the daughter plus the emitted particles weigh less than the parent. What is actually conserved is mass-energy: the missing mass has been converted to kinetic energy of the emitted particles via E = \Delta m \cdot c^2. The full balance includes both mass and kinetic energy.
- "The neutrino has no mass." The Standard Model of particle physics originally assumed so, but neutrino-oscillation experiments (Super-Kamiokande in Japan, SNO in Canada, KamLAND, and upcoming measurements at the India-based Neutrino Observatory at Theni) have shown that neutrinos have tiny masses — at most a fraction of an eV/c^2, millions of times smaller than the electron. So low that for the purposes of JEE beta-decay physics you can treat them as massless, but not exactly zero.
If JEE-level nuclear physics is what you need — the four decay modes, the balancing rules, the role of the neutrino, carbon dating — you have it. What follows is for readers who want the Gamow-factor derivation of alpha-decay lifetimes, a look at electron capture, Fermi's beta-decay theory, and an introduction to double beta decay (a process that might or might not violate lepton number).
Gamow's tunnelling model of alpha decay
The range of half-lives for alpha decay is staggering. ^{212}Po: 3\times 10^{-7} seconds. ^{232}Th: 1.4\times 10^{10} years. A factor of 10^{24} difference, for nuclei separated only by 20 units of A and a factor of about 2 in Q-value. Why?
George Gamow in 1928 gave the answer by describing the alpha particle as a quantum particle trapped inside the parent nucleus by a Coulomb barrier it cannot classically surmount. The alpha can escape only by tunnelling through the barrier. The tunnelling probability falls exponentially with the barrier's "Gamow factor":
with
where R is the nuclear radius, b is the classical turning point (where the Coulomb potential equals the alpha's energy), and V(r) = k(Ze)(2e)/r is the Coulomb potential outside the nucleus. Evaluating the integral gives a Gamow factor that depends on Z, A, and Q:
where Z_d is the daughter's atomic number, v is the alpha's velocity, and 137 is the inverse of the fine-structure constant. Small changes in E_\alpha produce enormous changes in G, which produce enormous changes in P_\text{tunnel} and hence in the half-life. The Geiger-Nuttall rule — an empirical observation that \log t_{1/2} is linear in 1/\sqrt{E_\alpha} across a decay chain — follows directly from this formula. Gamow's tunnelling model is one of the earliest and most successful applications of quantum mechanics to a macroscopic-looking observable.
Electron capture — the beta-plus alternative
When the beta-plus Q-value is less than 2 m_e c^2 = 1.022 MeV (including the created-positron mass), beta-plus decay is forbidden but the same nuclear transformation can still occur via electron capture (EC):
A K-shell (or occasionally L-shell) electron is absorbed by a proton in the nucleus, creating a neutron and emitting a single neutrino. There is no emitted positron, so the energy release need only exceed the electron's binding energy (of order keV) — much less than 1.022 MeV.
Experimental signatures of EC: the neutrino is invisible; what you see instead is the X-ray emission (and Auger electrons) from the daughter atom as its K-shell vacancy gets filled. These characteristic X-rays have the Moseley wavelengths you saw in the X-rays article. Beryllium-7 is a classic EC emitter: ^7Be + e^- → ^7Li + \nu_e, with a 53-day half-life; it is used as a tracer in environmental science.
Fermi's theory of beta decay — a four-fermion contact interaction
Fermi modelled beta decay in 1933 by analogy to electromagnetic radiation: a transition current at the nucleus emits a pair of leptons. His effective Hamiltonian density is
where G_F is Fermi's coupling constant, fitted to data as G_F \approx 1.166\times 10^{-5}\ \text{GeV}^{-2}. This four-fermion contact interaction is the low-energy limit of what we now know to be W-boson exchange in the electroweak theory. At nuclear energies (\sim MeV), the W boson (mass 80 GeV) is so heavy that its propagator looks like a point — Fermi's contact term is an excellent approximation.
Fermi's theory predicts the beta spectrum shape:
where F(Z, E_e) is the Fermi function accounting for the Coulomb distortion of the outgoing electron wave function near the daughter nucleus. This shape matches the observed beta spectra to exquisite precision — and deviations from it, at the very top of the spectrum (near E_e = Q), are what the KATRIN experiment in Germany is using to measure the electron antineutrino mass.
Neutrinoless double beta decay — would it rewrite physics?
In some even-even nuclei, ordinary single beta decay is energetically forbidden (because the daughter has higher mass than the parent) but double beta decay — two neutrons converting to two protons in a single event — is allowed:
This has been observed in a handful of nuclei (^{76}Ge, ^{100}Mo, ^{130}Te, ^{136}Xe) with half-lives around 10^{19}–10^{22} years — vastly longer than the age of the universe.
The more exotic version is neutrinoless double beta decay: two neutrons converting to two protons without emitting the antineutrinos, i.e., 0\nu\beta\beta:
This is allowed only if the neutrino is its own antiparticle (a Majorana fermion). Observing 0\nu\beta\beta would overturn the Standard Model's conservation of lepton number and would mean the neutrino generates its own mass through a new mechanism. No one has seen it — current limits on 0\nu\beta\beta half-lives are > 10^{26} years for ^{136}Xe, from experiments like KamLAND-Zen. The search continues; the Indian particle-physics community is part of the global effort, with the proposed INO-DBD programme aiming to contribute sensitivity from a tellurium-based detector.
The weak interaction and parity
Beta decay was the first process in which parity violation was observed — C. S. Wu's 1956 experiment with polarised ^{60}Co showed that the electrons from beta decay are preferentially emitted opposite to the spin direction of the parent nucleus. Nature distinguishes left from right in the weak interaction. This violation of mirror symmetry was a profound surprise (every other known interaction — gravity, electromagnetism, the strong force — respects parity) and earned T. D. Lee and C. N. Yang the 1957 Nobel. The modern explanation: the weak interaction couples only to left-handed particles and right-handed antiparticles. A neutrino is always left-handed; an antineutrino is always right-handed. This maximal parity violation is baked into the Standard Model.
Where this leads next
- Radioactive decay law and half-life — the exponential N(t) = N_0 e^{-\lambda t} and everything that follows.
- Mass defect and binding energy — the energy arithmetic that tells you which decays are allowed and which are forbidden.
- The nucleus — composition and size — the physical setting in which decays happen.
- Nuclear fission — a decay mode all its own, where the nucleus splits into two pieces of comparable size.
- Nuclear fusion — the opposite of fission; how small nuclei release energy by combining.