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

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, $1.67 \times 10^{-27}$ kg) and neutrons (0 charge, similar mass).

Notation $^A_Z X$: $Z$ atomic number (protons), $A$ mass number (protons + neutrons), $N = A - Z$ neutrons.

Isotopes. Same $Z$, different $N$. E.g., $^{12}$C, $^{13}$C, $^{14}$C.

Radioactive decay

Alpha

Emit helium nucleus $^4_2$He. Mass number drops 4, atomic number drops 2. Range: cm in air; stopped by paper.

Beta-minus

Neutron $\to$ 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:

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

$^{14}_6 \text{C} \to ^{14}_7 \text{N} + ^0_{-1} e + \bar{\nu}_e$ (beta-minus).

Half-life

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: $^{235}\text{U} + n \to ^{141}\text{Ba} + ^{92}\text{Kr} + 3n$, releasing $\sim 200$ MeV.

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

Fusion

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

Powers the sun. Controlled fusion remains research goal.

Examples in context

Example 1. ANSTO Mt Cotton's archived monazite samples include thorium-$232$ (half-life $1.4 \times 10^{10} \text{ years}$), which decays in a long chain ending at lead-$208$. Each alpha step lowers nucleon number by $4$ and proton number by $2$; each beta-minus step leaves nucleon number unchanged and raises proton number by $1$. Geologists use the parent-to-daughter ratio to date Queensland sapphire-bearing basalt fields north of Anakie, applying $N = N_0 (1/2)^{t/T_{1/2}}$. The QCAA Unit 1 nuclear summary expects students to balance such decay equations.

Example 2. Royal Brisbane Hospital cyclotron production of fluorine-$18$ ($T_{1/2} = 110 \text{ min}$) supplies PET scanners. A batch leaving the cyclotron with $20 \text{ GBq}$ at $0700$ has fallen to $20 \times (1/2)^{2.18} = 4.4 \text{ GBq}$ by the patient injection at $1100$. The isotope decays by positron ($\beta^+$) emission, the positrons annihilate with electrons and produce paired $511 \text{ keV}$ gammas detected coincidentally to localise tumours. The same dot-point isotope concept (same Z, different N) is the basis of all medical radio-tracers.

Try this

Q1. Define isotope and identify the decay particle that does not change the mass number. [2 marks]

• Cue. Isotope: same Z, different N; beta decay and gamma decay leave A unchanged.

Q2. Complete the alpha decay equation $^{226}_{88}\text{Ra} \rightarrow ?\text{Rn} + \alpha$. State the mass and charge of the alpha particle. [3 marks]

• Cue. $^{222}_{86}\text{Rn}$; alpha $= ^{4}_{2}\text{He}$, mass $\approx 4.00 \text{ u}$, charge $+2e$.

Q3. A $40 \text{ MBq}$ source of cobalt-$60$ ($T_{1/2} = 5.3 \text{ years}$) is purchased for radiotherapy. (a) Calculate the activity remaining after $15.9 \text{ years}$. (b) Cobalt-$60$ decays by beta-minus then gamma. Write the daughter nuclide and explain how the gamma originates. (c) Discuss one regulatory implication in Queensland of selecting an isotope with this half-life. [3+3+2 marks; ISMG: Knowledge and conceptual understanding, Evaluation]

• Cue. (a) Three half-lives, $5.0 \text{ MBq}$; (b) $^{60}\text{Ni}$ excited state emits gammas; (c) ARPANSA storage requirements.