Nuclear Physics and Radioactivity

🟢 Lite — Quick Review (1h–1d)

Rapid summary for last-minute revision before your exam.

Nuclear Physics and Radioactivity — Key Facts Radioactive decay law: $N = N_0 e^{-\lambda t}$; half-life $t_{1/2} = \frac{\ln 2}{\lambda} = \frac{0.693}{\lambda}$ Activity: $A = \lambda N = A_0 e^{-\lambda t}$; unit: becquerel (Bq) = 1 decay/s Alpha decay: $_Z^AX \rightarrow _{Z-2}^{A-4}Y + _2^4\alpha$ (loss of 2 protons + 2 neutrons) Beta decay: $_Z^AX \rightarrow _{Z+1}^AY + _{-1}^0\beta$ (neutron → proton + electron + antineutrino) Gamma decay: $_Z^AX^* \rightarrow _Z^AX + \gamma$ (excited nucleus loses energy) ⚡ Exam tip: In alpha decay, mass number decreases by 4; in beta decay, mass number unchanged

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🟡 Standard — Regular Study (2d–2mo)

Standard content for students with a few days to months.

Nuclear Physics and Radioactivity — JAMB Physics Study Guide Nuclear notation: $Z^AX$ where A = mass number (protons + neutrons), Z = atomic number (protons) Nuclear radius: $R = R_0 A^{1/3}$ where $R_0 = 1.2 \times 10^{-15}$ m Binding energy: $E = \Delta mc^2$ where $\Delta m = [Zm_p + Nm_n - M{nucleus}]$ Nuclear force: short-range (~10⁻¹⁵ m), charge-independent, strongest force in nature

Carbon dating: $^{14}C$ half-life = 5730 years; $^{14}C \rightarrow ^{14}N + \beta^-$; ratio of $^{14}C$ to $^{12}C$ in atmosphere is constant; measuring remaining $^{14}C$ in organic material gives age.

Nuclear fission: heavy nucleus splits into two medium nuclei + energy + neutrons; used in nuclear reactors; chain reaction requires critical mass.

Nuclear fusion: two light nuclei combine; releases more energy per unit mass than fission; powers the Sun: $4p \rightarrow He + 2e^+ + 2\nu + 2\gamma + 26.7$ MeV.

Common student mistakes: confusing activity with half-life (larger λ = shorter half-life = faster decay); forgetting that gamma decay doesn’t change A or Z; confusing fission and fusion.

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🔴 Extended — Deep Study (3mo+)

Comprehensive coverage for students on a longer study timeline.

Nuclear Physics and Radioactivity — Comprehensive Physics Notes

Radioactive decay — detailed treatment: The decay constant $\lambda$ is the probability per unit time that a given nucleus will decay. It is independent of temperature, pressure, and chemical state.

Activity units: 1 curie (Ci) = $3.7 \times 10^{10}$ Bq (original definition based on radium); 1 becquerel = 1 decay per second.

Decay chains: Some radioactive nuclei don’t decay directly to a stable nucleus. For example, $^{238}U \rightarrow ^{234}Th \rightarrow ^{234}Pa \rightarrow ^{234}U \rightarrow … \rightarrow ^{206}Pb$.

Energy in nuclear reactions: Mass defect: $\Delta m = Zm_p + (A-Z)m_n - M_{nucleus}$ Binding energy per nucleon: peaks around iron-56 (~8.8 MeV/nucleon), explaining why fission of heavy nuclei and fusion of light nuclei both release energy.

Radioactive dating formulas: For carbon dating: $t = \frac{1}{\lambda}\ln\left(\frac{R_0}{R}\right)$ where $R$ is the activity ratio of $^{14}C$ to $^{12}C$.

For potassium-argon dating (used in geology): $^{40}K \rightarrow ^{40}Ar$ (half-life = 1.25 billion years).

Half-life calculations: After $n$ half-lives: $N = N_0/2^n$; $A = A_0/2^n$. For sequential decay (parent → daughter → stable): apply separate decay laws for each species.

JAMB exam patterns:

• 2023 JAMB: If initial activity is 800 Bq and half-life is 4 hours, find activity after 16 hours
• 2022 JAMB: Alpha particle scattering experiment was done by Rutherford; what did it establish?
• 2021 JAMB: Calculate binding energy of helium-4 nucleus given masses
• 2020 JAMB: Nuclear fusion produces more energy than chemical reactions because…

Key values to memorise:

Particle	Mass (u)	Charge
Proton	1.00728	+e
Neutron	1.00867	0
Electron	0.00055	-e
Alpha	4.00260	+2e
1 u	931.5 MeV/c²	-

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📊 JAMB Exam Essentials

Detail	Value
Questions	180 MCQs (UTME)
Subjects	4 subjects (language + 3 for course)
Time	2 hours
Marking	+1 per correct answer
Score	400 max (used for university admission)
Registration	January – February each year

🎯 High-Yield Topics for JAMB

• Use of English (Grammar + Comprehension) — 60 marks
• Biology for Science students — 40 marks
• Chemistry (Organic + Physical) — 40 marks
• Physics (Mechanics + Optics) — 35 marks
• Mathematics (Algebra + Geometry) — 40 marks

📝 Previous Year Question Patterns

• Q: “The process of photosynthesis requires…” [2024 Biology]
• Q: “The electronic configuration of Fe is…” [2024 Chemistry]
• Q: “Find the value of x if 2x + 5 = 15…” [2024 Mathematics]

💡 Pro Tips

• Use of English carries the most weight — master grammar rules and comprehension strategies
• JAMB syllabus is your Bible — questions come directly from it. Download and use it.
• Past questions are highly predictive — repeat patterns appear every year
• For Science students, Biology and Chemistry are high-scoring if you study NCERT-level content

🔗 Official Resources

• JAMB Official
• JAMB Syllabus

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