Alpha, Beta, and Gamma Decay

Why alpha, beta, and gamma decay matter

• Three different forces, three different daughters. Alpha is mediated by the strong nuclear force tunneling through a Coulomb barrier; beta by the weak force changing flavour (n → p, ν̄_e); gamma by the electromagnetic force shedding excitation. The three modes change A by −4, 0, 0 and Z by −2, ±1, 0 respectively, making them genuinely independent decay channels.
• Half-lives span 30 orders of magnitude. ²¹²Po alpha-decays in 0.299 μs, ²³²Th in 1.40 × 10¹⁰ years. ¹³⁸La undergoes β⁻ at 1.05 × 10¹¹ years; the free neutron at 879.4 s. The Geiger-Nuttall law (1911) explains the alpha range as log₁₀(t₁/₂) ∝ Z/√Q via Gamow tunneling.
• Rutherford 1899-1903 classification by absorption. Aluminium foil 0.005 cm thick absorbed alphas; 1 mm absorbed betas; gammas required cm of lead. Rutherford coined "alpha" and "beta" in 1899; Paul Villard added "gamma" in 1900 by directing radium emission through a magnetic field — the deflectionless component was the gamma. Rutherford received the 1908 Nobel Prize in Chemistry.
• Pauli's neutrino solved the beta-spectrum crisis. James Chadwick's 1914 measurement of the ²¹⁴Bi beta spectrum showed a continuous distribution, not a discrete energy. Pauli's 1930 letter to Tübingen attendees proposed a "desperate remedy" — a neutral, near-massless particle carrying off the missing energy. Fermi's 1934 theory of beta decay turned this into a quantitative weak-interaction calculation that predicted half-lives correctly to within factors of 2-3.
• PET imaging exploits β⁺ annihilation. ¹⁸F (t₁/₂ = 109.8 min) decays by β⁺ to ¹⁸O. The positron annihilates with a tissue electron within ~1 mm, producing two back-to-back 511 keV photons. PET scanners detect coincident pairs to localize the decay; ¹⁸F-FDG (fluorodeoxyglucose) accumulates in glucose-hungry tumours. ~85 GBq of ¹⁸F is delivered per scan, half-life chosen to match ~1 hour transport plus ~1 hour imaging window.
• Smoke detectors use alphas from ²⁴¹Am. The 5.486 MeV alphas ionize air in a small chamber; smoke disrupts the ion current and triggers alarm. ~37 kBq (1 μCi) of ²⁴¹Am per detector — the alpha range of 4 cm in air confines the radiation but is sensitive enough to detect μg-per-m³ smoke particle loading.
• ⁶⁰Co teletherapy and gamma sterilization. ⁶⁰Co β⁻ decays (5.27 yr) into ⁶⁰Ni* which de-excites via two coincident gammas at 1.173 and 1.332 MeV — average 1.25 MeV, ideal for radiotherapy of deep tumours and for medical-product sterilization. A typical sterilization plant uses 1-3 MCi (37-111 PBq) of ⁶⁰Co.

Common misconceptions

• "Beta decay emits an electron from inside the nucleus." No — there are no electrons inside the nucleus. The weak interaction transmutes a down-quark to an up-quark, converting a neutron to a proton, with the electron and antineutrino created at the moment of the transition. The 1932 discovery of the neutron eliminated the older "nuclear-electron" hypothesis.
• "Gamma decay is just like X-rays." Photons are physically the same particle, but the source labels them: gamma = nuclear origin, X-ray = atomic-electron transition or bremsstrahlung. Energy ranges overlap heavily (X-rays go to ~150 keV in medical use; gammas can go below 10 keV from EC events). The terminology is historical.
• "Alpha decay can occur in any heavy nucleus." Q must be positive — the daughter plus alpha must weigh less than the parent. ²⁰⁸Pb (doubly magic) is alpha-stable despite Z = 82 because the binding-energy gain is below the alpha rest mass. Most alpha emitters cluster above Z = 83.
• "Beta-plus and electron capture are the same thing." Both convert p to n, lower Z by one, but β⁺ requires Q > 2m_e·c² = 1.022 MeV (positron rest mass plus daughter atomic-electron deficit) while EC has no kinetic threshold. ⁵⁵Fe (Q = 0.231 MeV) decays only by EC; ²²Na with Q = 2.84 MeV does both, with branching ratios set by phase space.
• "Half-life is a deterministic clock." Each individual nucleus decays as a Poisson process — its expected remaining lifetime never decreases. The half-life is a population statistic. Variance in counts per minute scales as √N, which is why low-activity samples need long count times.
• "Radioactivity always damages cells via direct ionization." Indirect damage via radiolysis-produced •OH radicals dominates for low-LET radiation (β, γ): about 60-70% of DNA strand breaks come from radicals reacting with bases, not from primary ionization tracks. Alphas are high-LET and damage directly along dense ionization columns; their relative biological effectiveness is ~20× that of gammas per Sv.

Process

Alpha decay is best described by Gamow's 1928 tunneling theory. Inside the parent nucleus, the alpha cluster sits in a potential well roughly −30 MeV deep, but is confined by a Coulomb barrier rising to V_C = 2(Z−2)e²/(4πε₀R) — about 28 MeV at R ≈ 1.2·A^(1/3) fm for ²³⁸U. Classically, an alpha with kinetic energy 4.27 MeV cannot escape; quantum mechanically it tunnels with probability P ∝ exp(−2π·η) where η is the Sommerfeld parameter, giving the Geiger-Nuttall relation log₁₀(t₁/₂) = a·Z/√Q + b. Half-lives stretch from 0.299 μs (²¹²Po, Q = 8.95 MeV) to 1.40 × 10¹⁰ y (²³²Th, Q = 4.08 MeV) — sensitivity of 10²⁴ to a factor of 2 change in Q.

Beta decay is governed by Fermi's 1934 theory of the weak interaction. At the quark level, a down quark in a neutron transitions to an up quark with emission of a virtual W⁻ that decays to e⁻ + ν̄_e. The decay rate is ω = (G_F²/2π³)·|M|²·f(Z,Q) where G_F = 1.166 × 10⁻⁵ GeV⁻² is the Fermi coupling, M is the nuclear matrix element, and f(Z,Q) is the Fermi integral over the kinematically available phase space ~ Q⁵. The Q⁵ dependence makes beta half-lives extremely sensitive to endpoint energy: free n at Q = 0.782 MeV has t₁/₂ = 879 s, while ¹⁴C at Q = 0.156 MeV has t₁/₂ = 5730 yr. Selection rules — allowed (ΔJ = 0,1; Δπ = no), first forbidden (ΔJ ≤ 2; Δπ = yes) — tag transitions by orders-of-magnitude variations in ft-value.

Gamma decay is the electromagnetic analogue: an excited nucleus drops to lower energy by photon emission. Multipole order Eℓ or Mℓ is set by angular momentum selection: Eℓ requires |J_i − J_f| ≤ ℓ ≤ J_i + J_f and parity change (−1)^ℓ; Mℓ requires the opposite parity. Transition rates scale as ω ∝ E_γ^(2ℓ+1)·R^(2ℓ)/ℏ²ᶜ²ˡ⁺¹, so E1 transitions (10⁻¹⁵ s) outpace E2 (10⁻⁹ s) by ~10⁶ at fixed energy. Isomers like ⁹⁹ᵐTc (J = 1/2⁻ → 9/2⁺ requires M4) live for hours because high multipole + low energy collapses the rate.

Decay modes side by side

Mode	Particle emitted	ΔA	ΔZ	Charge change	Spectrum	Penetration / stopping
Alpha (α)	⁴He nucleus (2p+2n)	−4	−2	+2e released	Discrete 4-9 MeV	~3.5 cm air, paper, dead skin layer
Beta-minus (β⁻)	e⁻ + ν̄_e	0	+1	+e released as e⁻	Continuous 0 to Q ≤ ~3 MeV	~3 m air at 1 MeV, mm of Al
Beta-plus (β⁺)	e⁺ + ν_e	0	−1	−e released as e⁺	Continuous 0 to Q − 1.022 MeV	~mm before annihilation to 511 keV pair
Electron capture (EC)	ν_e + characteristic X-rays	0	−1	K-shell vacancy fills	Monoenergetic ν, X-ray cascade	X-rays detected; primary ν undetected
Gamma (γ)	photon	0	0	None	Discrete 0.01-10 MeV lines	Exponential, half-thickness ~cm Pb
Internal conversion (IC)	K/L electron	0	0	K vacancy fills	Monoenergetic e⁻ at E_γ − BE	Like β but discrete; followed by X-rays
Spontaneous fission	2 fragments + 2-4 n + γ	~A/2 each	~Z/2 each	Charge split	~200 MeV total	Fragments stop in μm; neutrons in cm

Representative parent → daughter examples

Parent	Mode	Daughter	Q (MeV)	Half-life	Note
²³⁸U	α	²³⁴Th	4.270	4.468 × 10⁹ yr	Defines uranium-radium series
²²⁶Ra	α	²²²Rn	4.870	1600 yr	Curies' isolation 1898
²¹²Po	α	²⁰⁸Pb	8.954	0.299 μs	Steepest end of Geiger-Nuttall
n (free)	β⁻	p + e⁻ + ν̄_e	0.7824	879.4 s	Fundamental weak decay
¹⁴C	β⁻	¹⁴N	0.156	5700 yr	Radiocarbon dating
³H (tritium)	β⁻	³He	0.0186	12.32 yr	Endpoint used in KATRIN ν mass
²²Na	β⁺ (90%) + EC (10%)	²²Ne	2.842	2.602 yr	PET calibration source
⁶⁰Co	β⁻ then γ cascade	⁶⁰Ni	2.824	5.272 yr	1.173 + 1.332 MeV teletherapy
⁹⁹ᵐTc	γ (IT)	⁹⁹Tc	0.142	6.0058 hr	SPECT imaging workhorse

Penetration and shielding

Radiation	Range in air	Range in tissue	Shielding to halve	External hazard	Internal hazard
α (5 MeV)	~3.5 cm	~40 μm	Sheet of paper	None — stopped at skin	Severe (²¹⁰Po, ²³⁹Pu lung)
β⁻ (1 MeV)	~3 m	~5 mm	~2 mm aluminium	Skin and lens dose	Moderate (³H, ⁹⁰Sr bone)
β⁻ (³H, 18.6 keV max)	~6 mm	~6 μm	Skin layer	None	Moderate (HTO uptake)
γ (0.5 MeV)	Many m	Whole body	~0.5 cm Pb	Whole-body dose	Diffuse
γ (1.25 MeV ⁶⁰Co)	Many m	Whole body	~1.0 cm Pb	Whole-body dose	Diffuse
n (1 MeV)	Many m	Whole body	~5 cm hydrogenous	High RBE (~10×)	Activation products

Famous experiments and applications

• Becquerel 1896 — uranium salts on photographic plate. Henri Becquerel placed K₂UO₂(SO₄)₂ crystals on a wrapped photographic plate intending to study X-ray-induced phosphorescence; he discovered instead that uranium emitted penetrating radiation without external excitation. Nobel 1903 with Marie and Pierre Curie.
• Rutherford 1899 alpha and beta classification at McGill. Aluminium absorption curves split radium emission into a softly-absorbed component (alpha) and a hard component (beta). Rutherford and Royds 1908 confirmed alphas were ⁴He by collecting them in an evacuated thin-walled tube and detecting the He spectrum after several days; 1908 Nobel.
• Curies isolating polonium (1898) and radium (1902) from pitchblende. Several tons of Joachimsthal residue yielded ~0.1 g of RaCl₂ after fractional crystallization. Marie Curie won Nobels in Physics (1903) and Chemistry (1911) — the only person with Nobels in two sciences.
• Hans Geiger 1908 alpha-particle counter. First single-particle detector — a needle electrode in a gas-filled tube triggered audible clicks for individual alpha events. Geiger and Marsden's 1909 gold-foil experiment used this to count back-scattered alphas, leading Rutherford in 1911 to deduce the nuclear atom (10⁻¹⁵ m radius nucleus inside ~10⁻¹⁰ m atom).
• Iridium-192 industrial radiography sources. 75 days half-life, β⁻ to ¹⁹²Pt with prominent 296, 308, 316, 468 keV gammas. ~3.7 TBq sources weld-inspect pipelines and pressure vessels, exposing film through up to 75 mm of steel. Strict ALARA: source storage in 50 mm depleted uranium "pigs"; loss-of-source incidents in industrial radiography remain a leading cause of acute radiation injuries (e.g. Mayapuri 2010 Delhi).