Radioactivity: Types of Decay

Spec mapping: OCR H556 Module 6.4 — Nuclear and Particle Physics (alpha, beta-minus, beta-plus and gamma emission as decay modes of unstable nuclei; nuclear equations balancing nucleon number $A$A and proton number $Z$Z; penetrating power and ionising ability; lepton-number conservation requiring (anti)neutrinos in beta decay; PAG 10 anchor for absorption-of-radiation practical). Refer to the official OCR H556 specification document for exact wording.

Radioactivity was discovered at the end of the nineteenth century, when uranium salts left in a drawer were found to have fogged a photographic plate in the absence of any light. Within a few years, two new radioactive elements (polonium and radium) had been isolated, and the emissions had been classified into three distinct types based on how they were deflected by electric and magnetic fields. The three types were labelled with the first three letters of the Greek alphabet: $\alpha$α, $\beta$β and $\gamma$γ. Over a century later, those names are still in use — and the underlying physics is the heart of Module 6.4 — Nuclear and Particle Physics of the OCR A-Level Physics A specification (H556).

This lesson introduces the three principal modes of radioactive decay, together with the $\beta^{+}$β+ variant that becomes important in medical imaging later in the course, shows you how to write and balance nuclear equations, and sets out the typical properties and hazards of each type of radiation.

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What Is Radioactive Decay?

A radioactive nucleus is one that is unstable: it contains too many or too few neutrons for its proton number, or too much total mass, and it spontaneously transforms itself into a more stable configuration by emitting particles or photons. The transformation is governed by quantum mechanics and cannot be predicted for any individual nucleus — all we can say is the probability that a given nucleus will decay in a given time interval. This is the subject of the next lesson on the decay constant and half-life.

Decay is a spontaneous and random process. It is spontaneous in the sense that no external trigger is required: the nucleus rearranges itself from within. It is random in the sense that we cannot predict when a particular nucleus will decay — only the probability per unit time. Despite this randomness at the level of single nuclei, the behaviour of a large collection of nuclei is beautifully predictable, following a simple exponential law.

The OCR specification asks you to recognise and write equations for four kinds of decay:

• Alpha decay ($\alpha$α): emission of a helium-4 nucleus.
• Beta-minus decay ($\beta^{-}$β−): emission of an electron and an electron antineutrino.
• Beta-plus decay ($\beta^{+}$β+): emission of a positron and an electron neutrino.
• Gamma decay ($\gamma$γ): emission of a high-energy photon from an excited nucleus.

All four are examples of conservation laws in action. In every decay, electric charge is conserved, nucleon number is conserved, and (once neutrinos and antineutrinos are included) lepton number is also conserved. We shall see these rules in play shortly.

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Alpha Decay

In alpha decay, the nucleus emits an alpha particle, which is a helium-4 nucleus consisting of two protons and two neutrons. The alpha particle carries away 4 nucleons and 2 units of positive charge. The parent nucleus therefore loses 4 from its nucleon (mass) number $A$A and 2 from its proton (atomic) number $Z$Z:

$^{A}_{Z}\text{X} \to {}^{A-4}_{Z-2}\text{Y} + {}^{4}_{2}\text{He}$ZA​X→Z−2A−4​Y+24​He

A standard example is the alpha decay of uranium-238 to thorium-234:

$^{238}_{92}\text{U} \to {}^{234}_{90}\text{Th} + {}^{4}_{2}\text{He}$92238​U→90234​Th+24​He

Check the arithmetic: $238 = 234 + 4$238=234+4 (nucleon number conserved), $92 = 90 + 2$92=90+2 (charge conserved). Every balanced nuclear equation must pass these two simple checks.

Alpha particles are heavy (about 7300 times the mass of an electron) and doubly charged, so they interact strongly with matter and lose energy rapidly. A typical alpha particle travels only a few centimetres in air and is stopped by a sheet of paper or the outermost dead layer of skin. Alpha emitters are therefore harmless outside the body — but extremely dangerous if ingested or inhaled, because their short range concentrates all of the ionising energy into a tiny volume of living tissue.

Alpha decay tends to occur in very heavy nuclei ($Z > 82$Z>82), where the Coulomb repulsion between protons becomes comparable to the strong nuclear force holding the nucleus together. The alpha particle itself is an exceptionally tightly bound cluster — its $E_{B}/A$EB​/A is unusually large for so light a nucleus — which is why it is emitted intact rather than as two separate nucleons or four separate nucleons.

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Beta-Minus Decay

In beta-minus decay, a neutron inside the nucleus transforms itself into a proton, emitting an electron (the $\beta^{-}$β− particle) and an electron antineutrino. At the level of individual nucleons the elementary process is:

$n \to p + e^{-} + \bar{\nu}_{e}$n→p+e−+νˉe​

At the nuclear level, the nucleon number is unchanged (a neutron has become a proton, both being nucleons), while the atomic number increases by 1 (one extra proton):

$^{A}_{Z}\text{X} \to {}^{\ \ A}_{Z+1}\text{Y} + {}^{\ \ 0}_{-1}e + \bar{\nu}_{e}$ZA​X→Z+1  A​Y+−1  0​e+νˉe​

A classic example is the beta-minus decay of carbon-14:

$^{14}_{\ 6}\text{C} \to {}^{14}_{\ 7}\text{N} + {}^{\ \ 0}_{-1}e + \bar{\nu}_{e}$ 614​C→ 714​N+−1  0​e+νˉe​

Carbon-14 beta-decays to nitrogen-14 with a half-life of about 5730 years. This is the decay on which radiocarbon dating of biological material is based.

Beta-minus particles are fast-moving electrons, typically with kinetic energies of the order of 1 MeV. Because electrons are light, they have much longer ranges in matter than alpha particles — several metres in air and up to a few millimetres in aluminium. They ionise less densely and are less immediately dangerous externally, but they can still burn skin and damage tissue.

The antineutrino $\bar{\nu}_{e}$νˉe​ was first proposed in the 1930s to rescue conservation of energy and momentum in beta decay. Without it, the emitted electron would have a fixed energy (as the alpha particle in alpha decay does), but experiments showed that beta particles emerge with a continuous spectrum of energies up to some maximum. The neutrino carries the "missing" energy and momentum away almost invisibly. It was finally detected directly in the 1950s, decades after the original prediction.

Why an antineutrino and not a neutrino? Lepton number must be conserved. Before the decay the parent has lepton number $L = 0$L=0. After the decay, the daughter still has $L = 0$L=0, the emitted electron has $L = +1$L=+1, so the third product must have $L = -1$L=−1 — i.e. an anti-lepton. An electron antineutrino has $L_{e} = -1$Le​=−1 and ticks the box.

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Beta-Plus Decay

In beta-plus decay, a proton inside the nucleus transforms itself into a neutron, emitting a positron (the antiparticle of the electron, $e^{+}$e+) and an electron neutrino:

$p \to n + e^{+} + \nu_{e}$p→n+e++νe​

The atomic number decreases by 1 (one fewer proton), while the nucleon number is unchanged:

$^{A}_{Z}\text{X} \to {}^{\ \ A}_{Z-1}\text{Y} + {}^{0}_{+1}e + \nu_{e}$ZA​X→Z−1  A​Y++10​e+νe​

A standard example is the beta-plus decay of fluorine-18, the radiotracer used in PET scans (which we meet later in this module):

$^{18}_{\ 9}\text{F} \to {}^{18}_{\ 8}\text{O} + {}^{0}_{+1}e + \nu_{e}$ 918​F→ 818​O++10​e+νe​

Fluorine-18 beta-plus-decays to oxygen-18 with a half-life of about 110 minutes — conveniently short for medical use, long enough to prepare a dose at a regional cyclotron and inject it into a patient before it has all decayed away.

Beta-plus decay is less common than beta-minus decay overall but is vital in nuclear medicine. It only occurs in nuclei where the mass difference between parent and daughter exceeds $2 m_{e} c^{2}$2me​c2 (the rest energy of the emitted positron plus an electron that must effectively be accounted for in the atomic-mass bookkeeping). The lepton-number bookkeeping is the mirror image of $\beta^{-}$β−: the positron has $L_{e} = -1$Le​=−1, so the partner must be a (matter) neutrino with $L_{e} = +1$Le​=+1.

The emitted positron does not travel far. Within a millimetre or so it encounters an electron and annihilates, producing two 511 keV gamma photons travelling in opposite directions. It is these photons, not the positron itself, that PET scanners detect.

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Gamma Decay

In gamma decay, a nucleus in an excited state drops to a lower energy state, emitting the excess energy as a single high-energy photon (a gamma ray, $\gamma$γ):

$^{A}_{Z}\text{X}^{*} \to {}^{A}_{Z}\text{X} + \gamma$ZA​X∗→ZA​X+γ

The star $*$∗ denotes an excited nuclear state. Note that neither $A$A nor $Z$Z changes: the nucleus is the same species, just in a lower-energy configuration. Gamma emission is the nuclear analogue of the photon emission you met in atomic quantum physics, but with photon energies in the MeV range rather than the eV range.

A typical example is the decay of technetium-99m, the most widely used medical-imaging radioisotope:

$^{99m}_{\ \ \ 43}\text{Tc} \to {}^{99}_{43}\text{Tc} + \gamma \qquad (E_{\gamma} \approx 140\,\text{keV})$   4399m​Tc→4399​Tc+γ(Eγ​≈140keV)

The "m" stands for metastable: it is an excited state of Tc-99 that has an unusually long half-life of about 6 hours, long enough for it to be delivered from a generator at a regional nuclear-medicine facility and injected into a patient. When it decays it emits a 140 keV gamma photon, which is ideal for imaging — energetic enough to escape from inside the body, but not so energetic that it cannot be efficiently detected in a gamma camera.

Gamma rays are the most penetrating form of radiation. They can pass through several centimetres of lead and many metres of concrete; they are only attenuated, never fully stopped, by ordinary shielding (a result we shall quantify in the X-ray-imaging lessons via the Beer–Lambert law $I = I_{0} e^{-\mu x}$I=I0​e−μx). They are usually emitted alongside alpha or beta decay, as the daughter nucleus left in an excited state rearranges itself into its ground state.

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Summary Table of Decay Types

Decay	Particle emitted	$\Delta A$ΔA	$\Delta Z$ΔZ	Charge	Mass (u)	Range in air	Stopped by
Alpha $\alpha$α	${}^{4}_{2}\text{He}$24​He nucleus	$-4$−4	$-2$−2	$+2e$+2e	$\approx 4.00$≈4.00	few cm	paper / skin
Beta-minus $\beta^{-}$β−	electron + antineutrino	$0$0	$+1$+1	$-e$−e	$\approx 5.5 \times 10^{-4}$≈5.5×10−4	a few m	mm of aluminium
Beta-plus $\beta^{+}$β+	positron + neutrino	$0$0	$-1$−1	$+e$+e	$\approx 5.5 \times 10^{-4}$≈5.5×10−4	few mm	annihilates with $e^{-}$e−
Gamma $\gamma$γ	photon	$0$0	$0$0	$0$0	$0$0	many m	cm of lead (attenuated)

The values of $\Delta A$ΔA and $\Delta Z$ΔZ are the changes in nucleon number and proton number of the parent nucleus. A single nuclear event rarely involves more than one of these processes happening at the same time — but a given radioisotope may undergo several decays in succession, forming a decay chain.

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Penetrating Power — A Visual

Alpha is stopped by a sheet of paper. Beta-minus is stopped by a few millimetres of aluminium. Gamma is only attenuated, never completely stopped, by lead shielding — the question is one of intensity, governed by an exponential attenuation law we shall meet later in this module.

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Ionising Ability — Causal Chain

An inverse relationship holds between penetrating power and ionising ability per unit path length. Alpha particles, with their high charge ($+2e$+2e), low speed and strong electromagnetic coupling, ionise air very densely — of order $10^{5}$105 ion pairs per centimetre of track. Beta particles ionise perhaps a hundred times less densely. Gamma rays barely ionise at all directly; they transfer their energy mainly through Compton scattering or photoelectric absorption, in discrete events separated by centimetres of travel through the absorber.

Biologically, this has important consequences. Alpha radiation is the most dangerous if the source is internal — inside the lungs (radon daughters) or the gut — because it dumps its energy in a tiny volume of tissue, producing severe local damage. Gamma radiation is more dangerous externally because it penetrates deep into the body. Beta radiation is intermediate. Radiation protection therefore depends just as much on where the source is as on what it emits.

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Balancing Nuclear Equations

Every balanced nuclear equation must satisfy two rules:

1. Nucleon number conservation: the sum of the top numbers (nucleon numbers A) on the left equals the sum on the right.
2. Charge conservation: the sum of the bottom numbers (proton numbers Z) on the left equals the sum on the right.

Leptons (electrons, positrons, neutrinos, antineutrinos) have $A = 0$A=0, so they contribute nothing to the nucleon count. Electrons are written ${}^{\ \ 0}_{-1}e$−1  0​e (reflecting their charge); positrons are written ${}^{0}_{+1}e$+10​e. Neutrinos and antineutrinos have zero charge and zero nucleon number, so they do not appear in the $A$A/$Z$Z balancing — but you must still write them in to make the equation physically and lepton-number complete.

Worked Example 1 — Alpha decay of radium-226

Radium-226 alpha-decays. Write the full nuclear equation and identify the daughter nucleus.

The parent is ${}^{226}_{\ 88}\text{Ra}$ 88226​Ra. An alpha particle carries away 4 nucleons and 2 protons, so the daughter has $A = 226 - 4 = 222$A=226−4=222 and $Z = 88 - 2 = 86$Z=88−2=86. Element 86 is radon (Rn). Hence:

$^{226}_{\ 88}\text{Ra} \to {}^{222}_{\ 86}\text{Rn} + {}^{4}_{2}\text{He}$ 88226​Ra→ 86222​Rn+24​He

The daughter is radon-222, itself radioactive, and a significant member of the natural uranium decay chain — the source of the radon gas that accumulates in buildings constructed on granite bedrock.

Worked Example 2 — Beta-minus decay of strontium-90

Strontium-90 beta-minus-decays. Write the nuclear equation.

The parent is $^{90}_{38}\text{Sr}$3890​Sr. In beta-minus decay $A$A is unchanged and $Z$Z increases by 1, giving $^{90}_{39}\text{Y}$3990​Y (yttrium-90).

$^{90}_{38}\text{Sr} \to {}^{90}_{39}\text{Y} + {}^{\ \ 0}_{-1}e + \bar{\nu}_{e}$3890​Sr→3990​Y+−1  0​e+νˉe​

Check: $A$A: $90 = 90 + 0 + 0$90=90+0+0 $\checkmark$✓; $Z$Z: $38 = 39 + (-1) + 0$38=39+(−1)+0 $\checkmark$✓. Strontium-90 is a long-lived ($t_{1/2} \approx 29$t1/2​≈29 y) fission product that mimics calcium chemically, which is why it concentrates in bone if ingested.

Worked Example 3 — Beta-plus decay of sodium-22

Sodium-22 beta-plus-decays. Write the nuclear equation.

The parent is ${}^{22}_{11}\text{Na}$1122​Na. Beta-plus decay leaves $A$A unchanged and decreases $Z$Z by 1, giving ${}^{22}_{10}\text{Ne}$1022​Ne (neon-22).

$^{22}_{11}\text{Na} \to {}^{22}_{10}\text{Ne} + {}^{0}_{+1}e + \nu_{e}$1122​Na→1022​Ne++10​e+νe​

Check: $A$A: $22 = 22 + 0 + 0$22=22+0+0 $\checkmark$✓; $Z$Z: $11 = 10 + 1 + 0$11=10+1+0 $\checkmark$✓. Sodium-22 has a half-life of about 2.6 years and is a workhorse positron source in laboratory PET demonstrations.

Worked Example 4 — Decay chain of uranium-238

Uranium-238 decays via a long chain of alphas and betas, eventually reaching stable lead-206. How many alpha and beta-minus decays are involved in total?

The total changes are $\Delta A = 206 - 238 = -32$ΔA=206−238=−32 and $\Delta Z = 82 - 92 = -10$ΔZ=82−92=−10. Each alpha decay gives $\Delta A = -4$ΔA=−4, $\Delta Z = -2$ΔZ=−2; each beta-minus decay gives $\Delta A = 0$ΔA=0, $\Delta Z = +1$ΔZ=+1. Let $n_{\alpha}$nα​ be the number of alphas and $n_{\beta}$nβ​ the number of betas. Balancing $A$A first:

$-4\, n_{\alpha} = -32 \implies n_{\alpha} = 8.$−4nα​=−32⟹nα​=8.

Balancing $Z$Z:

$-2 n_{\alpha} + n_{\beta} = -10 \implies -16 + n_{\beta} = -10 \implies n_{\beta} = 6.$−2nα​+nβ​=−10⟹−16+nβ​=−10⟹nβ​=6.

So the uranium-238 chain involves 8 alpha decays and 6 beta-minus decays. This is the standard "$4n + 2$4n+2" decay series, and (via radium-226 and radon-222) is responsible for most of the natural background dose received in granite regions.

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Synoptic Links

• Conservation laws (Module 3.2 and Module 6.4): Every nuclear equation in this lesson is an exercise in conserving nucleon number, electric charge, and (with neutrinos/antineutrinos) lepton number. The same conservation framework underwrites collisions in mechanics, and energy/momentum conservation in particle-physics reactions later in the module.
• Photons and quantum behaviour (Module 4.5): Gamma emission is the nuclear analogue of atomic photon emission — same Planck relation $E = hf$E=hf, just $10^{6}$106 times higher energy. The 140 keV technetium-99m gamma is detected one quantum at a time in a gamma camera, exactly as visible photons are absorbed one at a time in the photoelectric effect.
• Antimatter and pair processes (Module 6.4, later lessons): The positron from $\beta^{+}$β+ decay annihilates with an electron to produce two back-to-back 511 keV photons — a process treated in detail in the annihilation-and-pair-production lesson and exploited directly in PET imaging.

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Specimen question modelled on the OCR H556 paper format

Question (9 marks): Polonium-210 is an alpha emitter, and strontium-90 is a beta-minus emitter. Both isotopes appear in trace amounts in the environment after nuclear accidents.

(a) (i) Write a balanced nuclear equation for the alpha decay of $^{210}_{\ 84}\text{Po}$ 84210​Po. State the daughter nuclide. [2]

(ii) Write a balanced nuclear equation for the beta-minus decay of $^{90}_{38}\text{Sr}$3890​Sr, including any neutrino or antineutrino emitted. State the daughter nuclide. [2]

(b) Polonium-210 emits an alpha particle of kinetic energy approximately $5.3$5.3 MeV. Compare the penetrating power and the ionising ability of this alpha particle with those of the beta particle from strontium-90 ($E_{\max} \approx 0.55$Emax​≈0.55 MeV). Refer to charge, mass and speed in your reasoning. [3]

(c) A piece of polonium-210, sealed inside a thin plastic envelope and placed against the skin, produces no measurable dose to the underlying tissue. The same source, if swallowed in microgram quantities, can be lethal. Explain this in terms of the properties of alpha radiation. [2]

AO breakdown

Mark	AO	Awarded for
1	AO2	$A$A and $Z$Z balance correctly for Po-210 → Pb-206 + He-4
2	AO1	Daughter identified as lead-206
3	AO2	$A$A and $Z$Z balance for Sr-90 → Y-90 + e⁻ + $\bar{\nu}_{e}$νˉe​
4	AO1	Daughter identified as yttrium-90, with antineutrino present
5	AO1	Alpha has greater charge ($+2e$+2e) and much greater mass than $\beta^{-}$β−
6	AO2	Hence shorter range / lower penetrating power for $\alpha$α
7	AO3	Higher ionising density for $\alpha$α (denser ion pairs per cm)
8	AO1	Outside skin, alpha is stopped by dead skin / plastic envelope — no dose
9	AO3	Internally, alpha dumps all 5.3 MeV into a tiny tissue volume — severe local damage

AO split: AO1 = 4, AO2 = 3, AO3 = 2.

Mid-band response (5/9):

(a) (i) $\text{Po-210} \to \text{Pb-206} + \alpha$Po-210→Pb-206+α. Daughter is lead-206.

(ii) $\text{Sr-90} \to \text{Y-90} + e^{-} + \bar{\nu}$Sr-90→Y-90+e−+νˉ. Daughter is yttrium-90.

(b) Alpha has more charge so it ionises more. Beta goes further because it is lighter.

(c) Alpha is stopped by skin, so it cannot hurt you outside, but inside the body it does damage.

Examiner commentary: The next-band move is to link mass, charge and speed to specific properties of penetration and ionisation, not just to assert them. Marks 1–4 awarded for both equations balanced with daughter named and antineutrino present. Mark 5 awarded for "alpha has more charge". Mark 6 awarded for "beta goes further". Marks 7–9 missed: the candidate does not articulate ionisation as ion pairs per cm, does not name the dead-skin layer or plastic envelope as the stopping medium, and does not link the internal danger to deposition of 5.3 MeV in a small tissue volume.

Stronger response (8/9):

(a) (i) $^{210}_{\ 84}\text{Po} \to {}^{206}_{\ 82}\text{Pb} + {}^{4}_{2}\text{He}$ 84210​Po→ 82206​Pb+24​He. Daughter is lead-206.

(ii) $^{90}_{38}\text{Sr} \to {}^{90}_{39}\text{Y} + {}^{\ \ 0}_{-1}e + \bar{\nu}_{e}$3890​Sr→3990​Y+−1  0​e+νˉe​. Daughter is yttrium-90.

(b) The alpha particle has charge $+2e$+2e and mass $\approx 7300\, m_{e}$≈7300me​; the beta particle has charge $-e$−e and mass $m_{e}$me​. The greater charge of the alpha means a much stronger Coulomb interaction with the electrons of atoms in its path, so it ionises much more densely — of order $10^{5}$105 ion pairs per cm in air, compared with $\sim 10^{3}$∼103 for the beta. The alpha is also much slower than a similar-energy beta (heavier mass), giving it more time to interact with each atom. The denser ionisation drains the alpha's kinetic energy much faster, so it stops within a few centimetres of air. The beta, ionising less densely and travelling faster, goes several metres in air.

(c) The plastic envelope and the few-micrometre dead layer of skin together absorb the entire range of the 5.3 MeV alpha. The underlying living tissue receives essentially no dose. Once inside the body — for instance dissolved in blood or absorbed in lung tissue — the alpha is in direct contact with living cells, and its short range concentrates all 5.3 MeV per particle into a microscopic volume of tissue, causing extensive DNA damage in a small group of cells.

Examiner commentary: To lift to top-band, the answer would make the causality explicit — that high ionising density follows from the combination of high charge, slow speed and the resulting prolonged dwell-time near each absorber atom — and would explicitly distinguish "no penetration through skin" (an alpha-only statement) from "no penetration through aluminium" (true also of beta). Marks 1–8 awarded; mark 9 partial because the candidate gestures at "small group of cells" without naming the tissue volume scale relative to a beta-emitter's spread-out dose.

Top-band response (9/9):

(a) (i) $^{210}_{\ 84}\text{Po} \to {}^{206}_{\ 82}\text{Pb} + {}^{4}_{2}\text{He}$ 84210​Po→ 82206​Pb+24​He. Balance check: $A$A: $210 = 206 + 4$210=206+4 $\checkmark$✓; $Z$Z: $84 = 82 + 2$84=82+2 $\checkmark$✓. The daughter is lead-206.

(ii) $^{90}_{38}\text{Sr} \to {}^{90}_{39}\text{Y} + {}^{\ \ 0}_{-1}e + \bar{\nu}_{e}$3890​Sr→3990​Y+−1  0​e+νˉe​. Balance check: $A$A: $90 = 90 + 0 + 0$90=90+0+0 $\checkmark$✓; $Z$Z: $38 = 39 - 1 + 0$38=39−1+0 $\checkmark$✓. Lepton-number check: before $L_{e} = 0$Le​=0; after $L_{e} = +1 - 1 + 0 = 0$Le​=+1−1+0=0 $\checkmark$✓. The daughter is yttrium-90 (itself a $\beta^{-}$β− emitter with $E_{\max} \approx 2.3$Emax​≈2.3 MeV).

(b) The alpha particle carries charge $+2e$+2e in a mass of $\approx 4\,\text{u}$≈4u; the beta particle carries charge $-e$−e in a mass of $m_{e} \approx 5.5 \times 10^{-4}\,\text{u}$me​≈5.5×10−4u. For comparable kinetic energies, the alpha is therefore very much slower than the beta, because $v = \sqrt{2 E_{k}/m}$v=2Ek​/m​. Three consequences follow. (1) Coulomb interaction is stronger for $\alpha$α because $|q|$∣q∣ is twice as large and the alpha lingers near each absorber atom for longer — denser ionisation (order $10^{5}$105 ion pairs cm$^{-1}$−1 in air, versus $\sim 10^{3}$∼103 for $\beta$β). (2) Penetration is shorter because that dense ionisation drains kinetic energy rapidly — a few cm in air, a few $\mu\text{m}$μm in tissue, versus several m of air and a few mm of aluminium for the beta. (3) Track structure differs: the alpha leaves a short, straight, densely ionised track; the beta leaves a longer, scattered, sparsely ionised track because it is light enough to be deflected significantly by atomic electrons.

(c) A 5.3 MeV alpha has a range of only $\approx 40\,\mu\text{m}$≈40μm in soft tissue and a fraction of a millimetre in plastic. The plastic envelope plus the dead, keratinised outer layer of skin (typically $20$20–$40\,\mu\text{m}$40μm) absorb the alpha completely, depositing all its energy in non-living material. The underlying living dermis receives zero dose. Once the polonium is ingested — distributed by blood, concentrated in liver, kidneys or bone marrow — each alpha is emitted in direct contact with living cells. The full 5.3 MeV is deposited within a sphere of $\approx 40\,\mu\text{m}$≈40μm radius, an absorbed dose density orders of magnitude higher than that delivered by an equivalent activity of beta emitter spread over millimetres. The biological effectiveness (RBE) of alpha is also higher because of its dense linear energy transfer. Microgram quantities are therefore lethal because they deliver many GBq of activity directly to radiosensitive tissues.

Examiner commentary: Full marks. The discriminator moves are (1) lepton-number bookkeeping made explicit in (a)(ii), (2) the causal chain charge → slow speed → dwell time → ionisation density → range, articulated in (b), and (3) the connection between range and dose density that explains why "no external risk, lethal internal risk" follows directly from alpha's $40\,\mu\text{m}$40μm range in tissue. Note the careful use of "$40\,\mu\text{m}$40μm" as a quantitative anchor and the appearance of RBE — both lift the answer above the qualitative ceiling of the stronger band.

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Common errors and mark-loss patterns

Pedagogical observations from teaching A-Level nuclear physics, with no fabricated examiner-report percentages.

• Forgetting the (anti)neutrino in beta-decay equations. OCR mark schemes require the (anti)neutrino to be written in explicitly. Lepton-number conservation is the stated reason, and lifting it out of the answer often costs a mark.
• Mixing up $\bar{\nu}_{e}$νˉe​ and $\nu_{e}$νe​. $\beta^{-}$β− goes with the antineutrino (the daughter electron has $L_{e} = +1$Le​=+1, partner must have $L_{e} = -1$Le​=−1); $\beta^{+}$β+ goes with the neutrino.
• "He" instead of $^{4}_{2}\text{He}$24​He for the alpha. The nucleon and charge numbers are required for the balance check; an unmarked "He" is not a credited symbol.
• Altering $A$A or $Z$Z for a gamma emission. Gamma decay is photon emission from the same nucleus in a lower-energy state — neither $A$A nor $Z$Z changes.
• "Radioactive decay is a chemical reaction". Loose language. Decay is a single-nucleus quantum process, independent of chemistry, temperature, pressure, or applied fields.
• "Alpha is the most dangerous radiation". Context-dependent. Externally, alpha is the least dangerous (stopped by dead skin); internally, alpha is the most dangerous (dense ionisation within $\sim 40\,\mu\text{m}$∼40μm of the source).
• Confusing electron with $\beta^{-}$β− symbolically. Both are written $^{\ \ 0}_{-1}e$−1  0​e in nuclear equations; the symbol is the beta particle once it has been emitted from the nucleus.
• Forgetting to convert MeV to joules. When the question wants energy in SI, $1\,\text{MeV} = 1.60 \times 10^{-13}\,\text{J}$1MeV=1.60×10−13J.
• Treating the antineutrino as merely "a label". It carries real energy and momentum — and explains the continuous beta-energy spectrum, which is itself an examinable feature of beta decay.

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Going further

The four classical decay modes are surface phenomena of much deeper physics that takes its full form at undergraduate level.

Alpha decay as quantum tunnelling. The alpha particle inside a heavy nucleus is bound by the strong force, but classically does not have enough energy to climb the Coulomb barrier between it and the rest of the nucleus. It escapes by tunnelling through that barrier — a wave-mechanical effect with no classical analogue. The Gamow-factor calculation of the tunnelling probability, derived in the 1920s, gives an exponential dependence on alpha energy that explains the spectacular range of alpha-emitter half-lives, from microseconds to billions of years, with energies varying by only a factor of two or three.

The weak interaction. Beta decay is mediated by the weak nuclear force, one of the four fundamental forces. At the quark level, $\beta^{-}$β− decay is $d \to u + W^{-} \to u + e^{-} + \bar{\nu}_{e}$d→u+W−→u+e−+νˉe​: a down quark inside a neutron emits a virtual $W^{-}$W− boson that immediately decays into an electron–antineutrino pair. The $W^{-}$W− is heavy ($\sim 80\,\text{GeV}/c^{2}$∼80GeV/c2), which is why beta decay is so slow compared with the strong and electromagnetic processes. The weak interaction is the only known process that does not conserve parity — a discovery that revolutionised our picture of fundamental symmetries.

The nuclear shell model. The unusual stability of $^{4}\text{He}$4He, $^{16}\text{O}$16O and $^{208}\text{Pb}$208Pb comes from filled shells at magic numbers of protons or neutrons (2, 8, 20, 28, 50, 82, 126). The shell model is the nuclear analogue of the atomic electronic shells and explains the local peaks on the binding-energy-per-nucleon curve, including the unusually stable $\alpha$α that emerges from $\alpha$α-decay processes.

Decay chains and the four series. Heavy nuclei lose nucleons four at a time (alpha) and adjust their proton number one at a time (beta), so every decay chain falls into one of four series labelled by $A \mod 4$Amod4: the thorium ($4n$4n), neptunium ($4n+1$4n+1, extinct), uranium ($4n+2$4n+2) and actinium ($4n+3$4n+3) series. Each terminates at a stable lead or bismuth isotope. The R-process nucleosynthesis in neutron-star mergers floods the heavy-element landscape with neutron-rich nuclei that beta-decay back toward stability along precisely these chains.

Oxbridge prompts.

1. "Why does a free neutron beta-decay with $t_{1/2} \approx 880$t1/2​≈880 s, but a neutron inside an oxygen-16 nucleus does not decay at all?" (Pauli blocking — the daughter proton would have to occupy an already-filled proton state in the daughter nucleus.)
2. "Estimate the order of magnitude of the alpha-decay lifetime of $^{238}\text{U}$238U ($E_{\alpha} \approx 4.3$Eα​≈4.3 MeV) given that of $^{214}\text{Po}$214Po ($E_{\alpha} \approx 7.7$Eα​≈7.7 MeV, $t_{1/2} \approx 164\,\mu\text{s}$t1/2​≈164μs)." (Gamow factor: lifetime ratio of order $10^{24}$1024.)
3. "Why is there no stable nucleus with $A = 5$A=5 or $A = 8$A=8? What does this imply for stellar nucleosynthesis?" (Triple-alpha bottleneck and the Hoyle resonance in $^{12}\text{C}$12C.)

Recommended undergraduate reading: Krane Introductory Nuclear Physics chapters 8 (alpha), 9 (beta) and 10 (gamma); Griffiths Introduction to Elementary Particles for the quark-level treatment of $\beta$β decay; Burcham and Jobes Nuclear and Particle Physics for the shell model.

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A-Level misconceptions

• "Binding-energy peak is at uranium because uranium is the biggest stable nucleus." Wrong. The binding-energy-per-nucleon peak is near iron-56, not at the heaviest nucleus. Fission of heavy nuclei and fusion of light nuclei both release energy precisely because both processes move nucleons toward the Fe-56 peak.
• "Mass defect is the mass lost by the nucleus during decay." No. The mass defect $\Delta m$Δm is the difference between the total mass of the separated nucleons and the mass of the assembled nucleus; $\Delta m > 0$Δm>0 for every bound nucleus, meaning the bound nucleus is lighter than its parts. Binding energy is $\Delta m \cdot c^{2}$Δm⋅c2.
• "Half-life equals $1/\lambda$1/λ." No. The half-life is $t_{1/2} = \ln 2 / \lambda \approx 0.693/\lambda$t1/2​=ln2/λ≈0.693/λ. The quantity $1/\lambda$1/λ is the mean lifetime, longer than the half-life by a factor of $1/\ln 2 \approx 1.44$1/ln2≈1.44.
• "$\beta^{-}$β− decay is $n \to p + e^{-}$n→p+e−." Incomplete. Lepton number requires an antineutrino: $n \to p + e^{-} + \bar{\nu}_{e}$n→p+e−+νˉe​. For $\beta^{+}$β+: $p \to n + e^{+} + \nu_{e}$p→n+e++νe​ (matter neutrino, because the positron is the anti-lepton).
• "Gamma decay changes the atom into a different element." No. Gamma emission is photon emission from a nuclear excited state. Neither $A$A nor $Z$Z changes — the nucleus simply de-excites.
• "$1\,\text{u} = 931.5\,\text{MeV}$1u=931.5MeV." Loose. The correct statement is $1\,\text{u} = 931.5\,\text{MeV}/c^{2}$1u=931.5MeV/c2, or equivalently $1\,\text{u}$1u has rest energy $931.5\,\text{MeV}$931.5MeV. This conversion factor is the workhorse of every nuclear-Q calculation.
• "Activity $A$A equals the number of nuclei $N$N." No. $A = \lambda N$A=λN. Activity (Bq, $\text{s}^{-1}$s−1) is the number of decays per second; $N$N is the population of undecayed nuclei. Both fall together at the same exponential rate, which is why $A/A_{0} = N/N_{0} = m/m_{0} = e^{-\lambda t}$A/A0​=N/N0​=m/m0​=e−λt for any sample.

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Summary

• Radioactivity is the spontaneous, random emission of particles or photons from unstable nuclei.
• Alpha decay emits a $^{4}_{2}\text{He}$24​He nucleus; $\Delta A = -4$ΔA=−4, $\Delta Z = -2$ΔZ=−2.
• Beta-minus decay emits an electron and an antineutrino; $\Delta A = 0$ΔA=0, $\Delta Z = +1$ΔZ=+1; the underlying process is $n \to p + e^{-} + \bar{\nu}_{e}$n→p+e−+νˉe​.
• Beta-plus decay emits a positron and a neutrino; $\Delta A = 0$ΔA=0, $\Delta Z = -1$ΔZ=−1; the underlying process is $p \to n + e^{+} + \nu_{e}$p→n+e++νe​.
• Gamma decay emits a high-energy photon from an excited nucleus; $\Delta A = 0$ΔA=0, $\Delta Z = 0$ΔZ=0.
• Every balanced nuclear equation conserves nucleon number, charge and lepton number.
• Alpha particles are stopped by paper, beta by a few mm of aluminium, gamma only attenuated by lead.
• Alpha is the most ionising and the most dangerous internally; gamma is the most penetrating and the most dangerous externally.

In the next lesson we put numbers on how fast a sample of radioactive nuclei decays, by introducing the decay constant $\lambda$λ and the half-life $t_{1/2} = \ln 2 / \lambda$t1/2​=ln2/λ.

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Reference: OCR A-Level Physics A (H556) specification 6.4 — Nuclear and Particle Physics (refer to the official OCR H556 specification document for exact wording).