Radioactivity: Alpha, Beta & Gamma

The three rays Becquerel and Rutherford sorted out are the working tools of a dozen modern fields. In medicine, gamma rays from cobalt-60 and technetium-99m image the body and destroy tumours; beta emitters are used in targeted radiotherapy; and the intensely local energy deposit of alpha particles makes alpha-emitting isotopes precision cancer weapons that spare the tissue a millimetre away. Smoke detectors in most homes contain a tiny americium-241 alpha source whose ionised air a whisper of smoke disrupts. Radiocarbon dating reads the beta activity of carbon-14 to date ancient wood and bone. Industry uses beta and gamma gauges to measure the thickness of paper, foil and plastic on the production line without touching them, and gamma radiography to X-ray welds and castings too thick for ordinary X-rays. Every one of these applications rests on exactly the properties this article compared — that alpha stops in tissue, beta penetrates a controlled few millimetres, and gamma passes through the body — and on the nuclear, temperature-proof constancy of the decay itself. The same penetration ranking dictates radiation shielding on spacecraft, in reactors, and around every hospital gamma source.

Start from what the previous article established: an atom's mass and all its positive charge live in a tiny central nucleus of protons and neutrons, bound by the strong nuclear force. Most nuclei are perfectly stable and sit there forever. But some combinations of protons and neutrons are unstable — the internal bookkeeping of energy and force does not quite balance — and such a nucleus will, sooner or later, rearrange itself into a more stable configuration and shed the excess as radiation. That spontaneous emission is radioactivity, and the rearrangement is a radioactive decay. Becquerel's uranium was doing exactly this in his drawer, and it had been doing it, and will keep doing it, for billions of years regardless of what anyone does to it. The single most important word here is nuclear. Ordinary chemistry — burning, dissolving, bonding — rearranges the outer electrons, and those processes trade energies of a few electronvolts. Radioactive decay reshuffles the nucleus itself, and nuclear energies are measured in millions of electronvolts (MeV), a factor of about a million larger. Heating a sample to red heat, cooling it in liquid nitrogen, crushing it, or locking its atoms into a compound changes the eV-scale electron cloud and leaves the MeV-scale nucleus completely indifferent. This is why the decay rate of a radioactive source is a fixed property of the nucleus, immovable by any everyday means — a fact we will turn into the exponential decay law two articles from now. The second key word is random. Radioactivity is genuinely probabilistic: identical nuclei, prepared the same way, decay at different, unpredictable moments. You cannot point at one uranium nucleus and say when it will go; you can only say what fraction of a large collection will have gone after a given time. The individual event is a roll of the quantum dice; only the statistics are lawful.

The very first thing early physicists did with Becquerel's radiation was pass it through a magnetic field, and it split into three beams. That single picture — reproduced above — already tells you almost everything: two of the rays are charged (they bend) and of opposite sign (they bend opposite ways), while the third is uncharged (it does not bend). The one that bends only slightly is heavy; the one that bends sharply is light. Reading those clues off, physicists worked out that the three rays are a helium nucleus, an electron, and a photon. The rest of this article is that identification, made quantitative.

Three particles, three identities. It is worth stating them plainly before comparing them, because every other property — charge, penetration, deflection — follows from what the thing is.

Alpha (α): a helium-4 nucleus, written $^{4}_{2}\text{He}$ — two protons and two neutrons bound tightly together. Its charge is $+2e$ and its mass is about $4\,u$, roughly four times a proton and nearly 7300 times an electron. Because it is a whole, tightly-bound nucleus, an alpha particle is emitted as a single compact projectile: slow (a few per cent of the speed of light), massive, and doubly charged.

Beta-minus (β⁻): an ordinary electron, charge $-e$, mass $m_e$ — the same electron you meet in circuits and atoms, but created in and flung out of the nucleus at the instant of decay (it was not orbiting there beforehand). Being nearly 7300 times lighter than an alpha, a beta particle of comparable energy travels far faster, up to $99\%$ of the speed of light, and carries far less momentum.

Gamma (γ): a photon — a quantum of electromagnetic radiation, the same kind of thing as light or an X-ray but of much higher energy. It has no charge and no rest mass, always travels at the speed of light $c = 3.0\times10^{8}\ \mathrm{m\,s^{-1}}$, and carries away energy in the MeV range. A gamma ray is emitted when a nucleus that is left in an excited state after an alpha or beta decay drops to a lower state, exactly as an atom emits a light photon when an electron falls between levels — but at nuclear, million-fold, energies. These three identities immediately fix the charges you will use in every deflection problem:

where: $e = 1.6\times10^{-19}\ \text{C}$ is the elementary charge. The physical reading is the whole story of the field experiment in one line: the alpha is doubly positive, the beta is singly negative, and the gamma is neutral. Opposite signs bend opposite ways; zero charge does not bend at all.

The three rays differ enormously in how far they travel through matter, and — crucially — the ranking of penetration is the exact reverse of the ranking of ionising power. Understanding why they are mirror images is the single most useful idea in this whole comparison. When a charged particle ploughs through matter it loses energy by knocking electrons off atoms — ionising them — and each such collision costs it a little energy. A slow, heavy, doubly-charged alpha interacts violently and constantly: it rips electrons off atoms thousands of times per millimetre, dumps all its energy within a very short distance, and so is stopped almost at once — a sheet of paper, the dead outer layer of your skin, or a few centimetres of air will halt it. But over that short path it creates a dense trail of ionisation, so alpha is by far the most ionising and the least penetrating. A beta particle, light and singly charged, interacts more gently. It ionises perhaps a hundred times less densely than an alpha, so it travels much further before it is spent — up to a few metres of air, and it takes a few millimetres of aluminium to stop it. Moderate ionisation, moderate penetration. A gamma ray carries no charge at all, so it does not steadily ionise as it goes; it interacts only in occasional, abrupt photon events. It therefore ionises very weakly but penetrates enormously — a gamma beam is attenuated by centimetres of lead or metres of concrete but, being absorbed statistically photon-by-photon, is never brought completely to zero, only reduced. Weakest ioniser, deepest penetrator.

where: the numbers are order-of-magnitude ratios of how many ion pairs each ray makes per unit path. The physical reading: penetration and ionisation are two sides of one coin. A ray that ionises fiercely spends its energy fast and so stops soon; a ray that barely ionises coasts a long way. That is why the danger ranking flips with geometry: outside the body gamma is the hazard (it reaches your organs while alpha is stopped by skin), but if an alpha emitter is inhaled or swallowed, alpha becomes the most dangerous, depositing all its energy in a tiny volume of tissue.

The experiment that unmasked the three rays was to fire the beam across a magnetic field and watch it fan out. A magnetic field exerts a force on a moving charge — and only on a moving charge — of magnitude $F = qvB$ when the velocity is perpendicular to the field, directed sideways (by the right-hand or Fleming rule) so that it always pushes the particle in a circle. Setting that magnetic force equal to the centripetal force $mv^2/r$ needed to hold the particle on a circle of radius $r$ gives the master relation of the whole experiment. Since gamma has $q = 0$, it feels no force and goes straight; the two charged rays curve, and because their charges have opposite sign they curve to opposite sides.

where: $q$ is the particle's charge magnitude, $v$ its speed, $m$ its mass, $B$ the field strength, $p = mv$ its momentum, and $r$ the radius of the circular arc it follows. The physical reading: the radius measures momentum per unit charge. A big, heavy, fast particle (large $p$) curves in a big lazy arc; a light particle of the same energy has much less momentum and curls up tightly. This is precisely why the heavy alpha bends only gently while the light beta bends sharply — and, with the sign of $q$, why they bend to opposite sides.

Board level — identify the three rays (CBSE and ICSE pattern)

A radioactive source is placed behind a slit so it emits a narrow beam. Three separate tests are run. (a) A sheet of paper placed in the beam removes one component entirely. (b) After the paper, a 4 mm aluminium plate removes a second component. (c) What remains passes through and is only cut down by a thick lead block. When a magnetic field is switched on, one component bends up, one bends down, one does not bend. Name each of the three rays and give its charge.

Step 1. The component stopped by mere paper is the least penetrating — the alpha ray, a helium nucleus of charge $+2e$. Alphas are halted by paper or the dead layer of skin.

Step 2. The component that survives paper but is stopped by a few millimetres of aluminium is the beta ray, an electron of charge $-e$. This aluminium test is the standard way to separate a beta emitter from a gamma emitter.

Step 3. The component that passes even the aluminium and is only reduced — never fully stopped — by centimetres of lead is the gamma ray, an uncharged photon.

Step 4. In the magnetic field the two charged rays bend to opposite sides because their charges have opposite sign; the alpha (heavy, $+2e$) bends only gently, the beta (light, $-e$) bends sharply the other way, and the uncharged gamma is undeflected, going straight. So the ray that does not bend is confirmed as gamma. Answer: α (+2e, stopped by paper), β (−e, stopped by aluminium), γ (0, only reduced by lead).

Competitive level — radius of an alpha's path in a magnetic field (JEE and NEET pattern)

A 5 MeV alpha particle enters a uniform magnetic field of 0.5 T at right angles to the field. Take the alpha's mass as 4 u = 6.64×10⁻²⁷ kg and its charge as +2e = 3.2×10⁻¹⁹ C. Find (a) its speed, and (b) the radius of its circular path. (c) State, without a full calculation, how a beta particle of the same energy would differ.

Step 1. Convert the energy: $KE = 5\ \text{MeV} = 5\times1.602\times10^{-13} = 8.01\times10^{-13}\ \text{J}$.

Step 2. The alpha's rest energy is about $3700\ \text{MeV}$, hugely more than $5\ \text{MeV}$, so it is non-relativistic and $KE = \tfrac12 m v^2$. Solve for the speed: $v = \sqrt{2\,KE/m} = \sqrt{2\times8.01\times10^{-13}/6.64\times10^{-27}} = \boxed{1.55\times10^{7}\ \mathrm{m\,s^{-1}}}$, about $5\%$ of $c$ — comfortably non-relativistic, as assumed.

Step 3. Apply $r = mv/(qB)$: $r = (6.64\times10^{-27})(1.55\times10^{7}) / \left[(3.2\times10^{-19})(0.5)\right] = \boxed{0.64\ \text{m}}$.

Step 4. A beta of the same 5 MeV has almost the same charge magnitude (within a factor of two) but a mass nearly $7300$ times smaller, so far less momentum $p = mv$; by $r = p/(qB)$ its radius is much smaller, and its negative charge curves it to the opposite side. So on the same photograph the alpha traces a broad gentle arc and the beta a tight opposite curl — the fingerprint that told the first experimenters they were seeing two different, oppositely-charged particles. Timing note: about 90 seconds. The one gate is remembering $r = mv/(qB)$ and that $v$ comes from $\tfrac12 mv^2 = KE$ — do the energy conversion first, then the square root, then one division. Do not reach for a relativistic formula on the alpha: a quick "$5\ \text{MeV} \ll$ rest energy" check licenses the clean non-relativistic route and saves you minutes. The part-(c) comparison needs no arithmetic at all — it is worth full marks for the two words "smaller, opposite".

Penetration ranked backwards. The order is $\gamma > \beta > \alpha$ for penetration and the reverse, $\alpha > \beta > \gamma$, for ionising power. Writing "alpha penetrates most because it is most energetic" is the classic slip — alpha is stopped by paper. Anchor it: paper stops α, a few mm of aluminium stops β, centimetres of lead only reduce γ. Tested on CBSE, ICSE, IGCSE, AP-2 and A-Level every year.

Saying gamma is "never stopped, so infinitely penetrating" or "completely blocked by lead". Neither. A gamma beam is attenuated exponentially — each thickness of lead cuts it by the same factor, so it is steadily reduced but, mathematically, never brought exactly to zero. Lead does not "stop" gamma; it thins it. (The exponential form is the decay-law article's job.)

The beta electron "was orbiting in the nucleus". No — the emitted electron is created at the moment of decay when a neutron turns into a proton; it was not sitting inside the nucleus beforehand. Do not describe beta decay as the nucleus "losing one of its orbital electrons".

Getting the deflection directions wrong, or bending the gamma. Alpha ($+2e$) and beta ($-e$) bend to opposite sides; gamma ($q=0$) does not bend at all. A diagram that curves the gamma, or bends α and β the same way, throws away easy marks. And the alpha bends less than the beta despite its larger charge, because it is so much heavier (bigger momentum, bigger radius).

Claiming temperature, pressure or chemistry changes the decay rate. They do not — radioactivity is nuclear (MeV) and untouched by eV-scale conditions. "Heating the sample speeds up decay" is always wrong.

Board scope. The qualitative comparison here — the three rays, their charges, penetration, and magnetic deflection — is on every board including IGCSE 0625, which carries this half of nuclear physics. The quantitative pieces (the MeV-to-joule conversion, $r = mv/(qB)$ radius calculations, and the exponential attenuation of gamma) are for CBSE, ICSE (ISC), JEE Main and Advanced, NEET, AP-2, IB HL and A-Level 9702 — IGCSE and IB SL keep the description but not the algebra.

Texts. NCERT Physics Class 12, Chapter 13 ("Nuclei"), the radioactivity sections · H. C. Verma, Concepts of Physics Vol. 2, "The Nucleus" · Halliday, Resnick and Walker, "Nuclear Physics" · Krane, Introductory Nuclear Physics, for the historical route and the deflection experiments.

Provenance. Standard nuclear constants ($e = 1.6\times10^{-19}\ \text{C}$, $u = 1.66\times10^{-27}\ \text{kg}$, $m_e = 9.11\times10^{-31}\ \text{kg}$, $c = 3.0\times10^{8}\ \mathrm{m\,s^{-1}}$, $1\ \text{MeV} = 1.602\times10^{-13}\ \text{J}$). Recompute: $q_\alpha = +2e = 3.2\times10^{-19}\ \text{C}$, $q_\beta = -e = -1.6\times10^{-19}\ \text{C}$, $q_\gamma = 0$; alpha mass $4\,u = 6.64\times10^{-27}\ \text{kg}$, mass ratio $\alpha/\beta \approx 7300$; ionising ratio $\alpha:\beta:\gamma \approx 10^{4}:10^{2}:1$; 5 MeV $= 8.01\times10^{-13}\ \text{J}$, $v_\alpha = \sqrt{2KE/m} = 1.55\times10^{7}\ \mathrm{m\,s^{-1}} \approx 0.05c$, $r_\alpha = mv/(qB) = 0.64\ \text{m}$ at $B = 0.5\ \text{T}$; equal-momentum radius ratio $r_\alpha/r_\beta = q_\beta/q_\alpha = 1/2$ — all recomputed in verify_hs2-radioactivity-alpha-beta-gamma.py.

Prerequisites. Inside the Nucleus: Protons, Neutrons & Isotopes — what the nucleus is made of and why some combinations are unstable. Leads to. Alpha Decay & the Q-Value, which takes the alpha ray apart in energy detail (the Q-value, why a whole helium nucleus, and Gamow tunnelling by name); and, further on, Beta Decay & the Neutrino, Gamma Decay & Nuclear Energy Levels, and The Radioactive Decay Law, which turns the "random, nuclear" nature established here into the exponential $N = N_0 e^{-\lambda t}$. For enrichment, the university seam on particle-decay kinematics (go-deeper only, never an exam dependency here).