describe the composition, mass and charge of α-, β- and γ-radiations (both β– (electrons) and β+ (positrons) are included)

Atoms, Nuclei and Radiation – Cambridge 9702 (A‑Level)

Learning Objective

Describe the composition, mass and charge of the three main types of nuclear radiation (α, β⁻, β⁺ and γ). Write correct decay equations (including neutrinos/antineutrinos), state the relevant conservation laws and recognise the characteristic energy spectra of α‑ and β‑radiations.

1. Nuclear Model & Rutherford Scattering (Syllabus 11.1)

• Rutherford’s α‑scattering experiment (1911) showed that most of the atom is empty space and that a tiny, massive, positively‑charged nucleus (≈ 10⁻¹⁴ m radius) resides at the centre.
• α‑particles (He‑2 nuclei) from a radioactive source were directed at a thin gold foil. Most passed straight through, but a few were deflected at large angles, proving the existence of a concentrated positive charge.

Suggested diagram: a beam of α‑particles incident on a gold foil with some particles scattered at wide angles, indicating a compact nucleus.

2. Nucleon Number (A) and Proton Number (Z)

• A (mass number) = total number of nucleons (protons + neutrons) in the nucleus.
• Z (atomic number) = number of protons; also the charge of the nucleus in units of the elementary charge e.
• Both A and Z are conserved in nuclear reactions (except that A can change by 4 in α‑decay, Z by ±1 in β‑decay, but the total before and after remains the same).

3. Isotopes & Nuclear Notation

An isotope is a nuclide with the same Z (same element) but a different A (different number of neutrons).

In a decay the superscript (A) and subscript (Z) change according to the type of radiation emitted, while the element symbol (X) may change when Z changes.

4. Radiation Types – Composition, Mass, Charge & Penetration

5. Decay Equations (including neutrinos)

5.1 Alpha Decay

General form

\[

{}^{A}{Z}\!X \;\longrightarrow\; {}^{A-4}{Z-2}\!Y \;+\; {}^{4}_{2}\!He\;(\alpha)

\]

Example (uranium‑238)

\[

{}^{238}{92}\!U \;\longrightarrow\; {}^{234}{90}\!Th \;+\; {}^{4}_{2}\!He

\]

5.2 Beta‑Minus Decay

\[

{}^{A}{Z}\!X \;\longrightarrow\; {}^{A}{Z+1}\!Y \;+\; e^{-} \;+\; \bar{\nu}_{e}

\]

Example (carbon‑14)

\[

{}^{14}{6}\!C \;\longrightarrow\; {}^{14}{7}\!N \;+\; e^{-} \;+\; \bar{\nu}_{e}

\]

5.3 Beta‑Plus Decay (Positron Emission)

\[

{}^{A}{Z}\!X \;\longrightarrow\; {}^{A}{Z-1}\!Y \;+\; e^{+} \;+\; \nu_{e}

\]

Example (fluorine‑18)

\[

{}^{18}{9}\!F \;\longrightarrow\; {}^{18}{8}\!O \;+\; e^{+} \;+\; \nu_{e}

\]

5.4 Electron Capture (alternative to β⁺)

\[

{}^{A}{Z}\!X \;+\; e^{-}{\text{(K or L shell)}} \;\longrightarrow\; {}^{A}{Z-1}\!Y \;+\; \nu{e}

\]

Example (beryllium‑7)

\[

{}^{7}{4}\!Be \;+\; e^{-} \;\longrightarrow\; {}^{7}{3}\!Li \;+\; \nu_{e}

\]

5.5 Gamma Emission

\[

{}^{A}{Z}\!X^{*} \;\longrightarrow\; {}^{A}{Z}\!X \;+\; \gamma

\]

\({}^{A}_{Z}\!X^{*}\) denotes an excited nucleus that de‑excites by emitting a photon.

6. Conservation Checks (quick reference)

• Mass number (A): unchanged in α, β⁻, β⁺, electron capture and γ decays (the emitted particle’s A is accounted for).
• Charge (Z): conserved when the charge of the emitted particle is included (+2 for α, –1 for β⁻, +1 for β⁺, 0 for γ).
• Energy: total decay energy is shared between kinetic energy of the emitted particles and (anti)neutrinos; for γ‑rays it appears as photon energy.
• Linear momentum: conserved; in two‑body α‑decay the daughter nucleus recoils opposite the α‑particle.

7. Energy Spectra – Why They Differ

• α‑particles: Two‑body decay → fixed Q‑value → α‑particle emerges with a single kinetic energy (discrete line).
• β‑particles (β⁻ and β⁺): Three‑body decay (daughter + β + (anti)neutrino) → kinetic energy is shared continuously → continuous spectrum from 0 up to a maximum \(E_{\max}\).
• γ‑rays: Emitted when an excited nucleus drops to a lower energy level → photon energy equals the exact difference between the two nuclear levels (discrete lines).

8. Compact Summary Table

9. Common Misconceptions

1. “All radiation is equally dangerous.” – α particles cannot penetrate skin; they are hazardous only if ingested or inhaled. β particles can cause skin burns, while γ rays are the most penetrating and require dense shielding.
2. “β‑radiation is just electrons.” – β⁻ are electrons; β⁺ are positrons (the electron’s antimatter counterpart) and annihilate with electrons, producing 511 keV γ‑rays.
3. “γ‑rays are particles.” – They are high‑energy photons, i.e., quanta of electromagnetic radiation, not matter particles.
4. “Neutrinos carry charge.” – Neutrinos and antineutrinos are electrically neutral; they escape the nucleus carrying away energy and angular momentum.

10. Key Equations for the Syllabus

• Mass–energy equivalence: \(E = mc^{2}\)
• Charge conservation: \(\displaystyle\sum Q{\text{initial}} = \sum Q{\text{final}}\)
• Energy balance in β‑decay (three‑body): \(Q = T{\beta} + T{\nu} + (m{\text{daughter}}-m{\text{parent}})c^{2}\)

11. Suggested Classroom Diagram

A single illustration showing a nucleus emitting:

• (i) an α‑particle (large, +2 e, short arrow, labelled “α”),
• (ii) a β⁻ electron (small, –1 e, longer arrow, labelled “β⁻”),
• (iii) a β⁺ positron (small, +1 e, labelled “β⁺”),
• (iv) a γ‑photon (wavy line, labelled “γ”).

Next to each arrow indicate relative size, charge symbol, typical shielding material and, for β⁺, the annihilation γ‑rays.