← Unit 1: Thermal, nuclear and electrical physics

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What is nuclear physics, and how do nuclei decay and produce energy?

Atomic nucleus, isotopes, types of radioactive decay (alpha, beta, gamma), half-life, fission and fusion

A focused answer to the QCE Physics Unit 1 subject-matter point on nuclear physics. Atomic structure, isotopes, alpha/beta/gamma decay, half-life formula $N = N_0(1/2)^{t/T_{1/2}}$, fission and fusion.

Generated by Claude OpusReviewed by Better Tuition Academy8 min answer

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What this dot point is asking

QCAA wants Year 11 students to describe atomic structure, recognise radioactive decay types, and apply the half-life formula.

Atomic structure

Nucleus: protons (+e, 1.67Γ—10βˆ’271.67 \times 10^{-27} kg) and neutrons (0 charge, similar mass).

Notation ZAX^A_Z X: ZZ atomic number (protons), AA mass number (protons + neutrons), N=Aβˆ’ZN = A - Z neutrons.

Isotopes. Same ZZ, different NN. E.g., 12^{12}C, 13^{13}C, 14^{14}C.

Radioactive decay

Alpha. Emit helium nucleus 24^4_2He. Mass number drops 4, atomic number drops 2. Range: cm in air; stopped by paper.

Beta-minus. Neutron β†’\to proton + electron + antineutrino. Atomic number increases by 1; mass number unchanged. Range: metres in air; stopped by aluminium.

Gamma. High-energy photon from excited nucleus. Mass and atomic numbers unchanged. Highly penetrating; lead/concrete shielding.

Nuclear equations

Conservation: mass number and charge conserved on both sides.

Examples:

92238U→90234Th+24He^{238}_{92} \text{U} \to ^{234}_{90} \text{Th} + ^4_2 \text{He} (alpha).

614Cβ†’714N+βˆ’10e+Ξ½Λ‰e^{14}_6 \text{C} \to ^{14}_7 \text{N} + ^0_{-1} e + \bar{\nu}_e (beta-minus).

Half-life

N=N0(12)t/T1/2N = N_0 \left(\frac{1}{2}\right)^{t/T_{1/2}}

Half-life is statistical; random for individual atom.

Common: C-14 (5,730 yr, carbon dating), I-131 (8 days, medical), U-238 (4.5 Gyr).

Fission

Heavy nucleus splits: 235U+nβ†’141Ba+92Kr+3n^{235}\text{U} + n \to ^{141}\text{Ba} + ^{92}\text{Kr} + 3n, releasing ∼200\sim 200 MeV.

Chain reaction possible (more than one neutron per fission triggers next).

Fusion

Light nuclei combine: 2H+3Hβ†’4He+n^2\text{H} + ^3\text{H} \to ^4\text{He} + n, ∼17.6\sim 17.6 MeV.

Powers the sun. Controlled fusion remains research goal.

Common errors

Non-conservation in nuclear equations. Both mass number and charge must balance.

Confusing decay types. Alpha: heavy, slow. Beta: fast electron. Gamma: photon.

Half-life as deterministic. Individual decay is random.

In one sentence

Nuclei contain protons and neutrons; unstable nuclei undergo alpha (emit He nucleus), beta-minus (neutron to proton plus electron plus antineutrino) or gamma (photon) decay; the half-life formula N=N0(1/2)t/T1/2N = N_0 (1/2)^{t/T_{1/2}} describes statistical decay over time, fission of heavy nuclei (uranium) and fusion of light nuclei (hydrogen) release energy by converting mass to energy (E=mc2E = mc^2).

Past exam questions, worked

Real questions from past QCAA papers on this dot point, with our answer explainer.

Year 11 SAC4 marksCarbon-14 has half-life $5,730$ years. (a) Atoms remaining after $11,460$ years from $10^{10}$ initial? (b) Write the beta-minus decay equation.
Show worked answer β†’

(a) 11460/5730=211460/5730 = 2 half-lives. N=1010(1/2)2=2.5Γ—109N = 10^{10} (1/2)^2 = 2.5 \times 10^9 atoms.

(b) 614Cβ†’714N+βˆ’10e+Ξ½Λ‰e^{14}_6 \text{C} \to ^{14}_7 \text{N} + ^0_{-1} e + \bar{\nu}_e.

Charge: 6 = 7 + (-1). Mass: 14 = 14 + 0. Conserved.

Markers reward half-life calculation and conservation in nuclear equation.

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