Nuclear Physics

🟢 Lite — Quick Review (1h–1d)

Rapid summary for last-minute revision before your MDCAT exam.

What is Nuclear Physics? Nuclear Physics deals with the structure, properties, and reactions of atomic nuclei. Key topics for MDCAT include radioactivity, nuclear reactions, binding energy, and nuclear fission/fusion.

Key Definitions:

Nuclide notation: $_Z^A X$ where $A$ = mass number (protons + neutrons), $Z$ = atomic number (protons)

Isotopes: Same $Z$ (same element), different $A$ (different neutron number). Example: $^{12}\text{C}$ and $^{14}\text{C}$

Radioactive Decay Laws:

• Activity $A = \lambda N$ (Bq)
• Decay constant $\lambda$ (per second)
• $N = N_0 e^{-\lambda t}$
• Half-life $t_{1/2} = \frac{\ln 2}{\lambda} = \frac{0.693}{\lambda}$
• Mean life $\tau = \frac{1}{\lambda} = \frac{t_{1/2}}{0.693}$

⚡ MDCAT Tip: In half-life problems, remember: after $n$ half-lives, remaining fraction = $(1/2)^n$. After 3 half-lives, only 1/8 of original remains.

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🟡 Standard — Regular Study (2d–2mo)

For students who want genuine understanding.

Types of Radioactive Emission:

Alpha particles ($\alpha$): Helium nucleus $_2^4\text{He}$, charge +2e, heavy, low penetration (stopped by paper), highly ionising. When a nucleus emits α, its mass number decreases by 4 and atomic number decreases by 2. $$_Z^A X \rightarrow _{Z-2}^{A-4} Y + _2^4\alpha$$

Beta particles ($\beta^-$): High-speed electrons from neutron decay inside the nucleus. $n \rightarrow p + e^- + \bar{\nu}_e$. Charge −1e, moderate penetration (stopped by thin Al). Increases atomic number by 1. $$_Z^A X \rightarrow _{Z+1}^A Y + _{-1}^0\beta + \bar{\nu}_e$$

Gamma rays ($\gamma$): High-energy electromagnetic radiation, no charge, very high penetration (stopped by thick lead/concrete). Often emitted after α or β decay when the daughter nucleus is in an excited state and releases energy as γ.

Gamma decay: $_Z^A X^* \rightarrow _Z^A X + \gamma$ (no change in Z or A)

Radioactive Decay Series: Uranium-238 decay series: $^{238}\text{U} \rightarrow \cdots \rightarrow ^{206}\text{Pb}$ (stable). This involves multiple α and β decays and is important for understanding geological dating.

Nuclear Reactions: Balance mass number ($A$) and atomic number ($Z$) on both sides: $$_Z^A X + _z^a x \rightarrow _{Z+z}^{A+a} Y + \text{energy}$$

Q-value (Energy of Reaction): $$Q = [m_{\text{reactants}} - m_{\text{products}}]c^2 \text{ (in MeV)}$$

• $Q > 0$: Exothermic (releases energy)
• $Q < 0$: Endothermic (requires energy)

Fission and Fusion:

• Nuclear fission: Heavy nucleus (e.g., $^{235}\text{U}$) splits into lighter nuclei + energy + neutrons. Produces ~200 MeV per fission. Chain reaction occurs if critical mass is maintained.
• Nuclear fusion: Light nuclei (e.g., D + T) fuse to form heavier nucleus + energy. Produces more energy per unit mass than fission but requires extremely high temperatures (~10⁸ K).

⚡ MDCAT Tip: Fusion produces MORE energy per kilogram than fission. This is why the Sun and hydrogen bombs work. However, fusion requires nuclei to overcome Coulomb repulsion — hence the extreme temperature requirement.

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🔴 Extended — Deep Study (3mo+)

Comprehensive coverage for students on a longer study timeline.

Binding Energy — Why Nuclei Are Stable: The mass of a nucleus is always less than the sum of masses of its constituent nucleons. The mass difference (mass defect $\Delta m$) is converted to binding energy via Einstein’s equation: $$E = \Delta m \cdot c^2$$

Binding energy per nucleon curve:

• Plot binding energy per nucleon vs mass number — peak at iron-56 (~8.8 MeV/nucleon)
• Nuclei lighter than Fe release energy through fusion (combining)
• Nuclei heavier than Fe release energy through fission (splitting)
• This is why iron is the most stable nucleus

Nuclear Stability: A nucleus is stable when the ratio of neutrons to protons is in the right range:

• For light nuclei (Z ≤ 20): N/Z ≈ 1
• For heavy nuclei (Z > 80): N/Z ≈ 1.5 (need more neutrons to counteract increasing Coulomb repulsion)
• Magic numbers (2, 8, 20, 28, 50, 82, 126) represent complete nuclear shells — these nuclei are especially stable

Radioactive Dating:

• Carbon-14 dating: Used for archaeological samples (up to ~50,000 years). Living organisms maintain a constant C-14/C-12 ratio. After death, C-14 decays with half-life of 5730 years. $$t = \frac{\ln(R_f/R)}{\lambda}$$

• U-Pb dating: Used for geological timescales (billions of years). Uranium-238 decays to lead-206 with half-life of 4.5 billion years.

Particle Accelerators — Cyclotron: A cyclotron uses perpendicular electric and magnetic fields to accelerate charged particles in a spiral path:

• Frequency of revolution: $f = \frac{qB}{2\pi m}$ (independent of speed and radius)
• Maximum energy: $E_{max} = \frac{q^2B^2r_{max}^2}{2m}$

⚡ MDCAT Pattern: MDCAT frequently asks about the properties of α, β, γ emissions (penetration power, ionising ability, deflection in magnetic fields). Also common: half-life calculations with sequential decay.

Detection of Radiation:

• Geiger-Müller (GM) counter: Detects ionisation current from radiation
• Cloud chamber: Shows tracks of ionising particles
• Film badge: Uses photographic film to measure radiation exposure

Medical Applications:

• Radiotherapy: Gamma rays used to destroy cancer cells
• Radioisotope imaging: Technetium-99m used in PET scans
• Sterilisation: Gamma rays kill bacteria in medical equipment

MDCAT Common Mistakes:

1. Confusing alpha decay: daughter nucleus has Z-2, A-4 (lost 2 protons AND 2 neutrons)
2. Forgetting that gamma rays carry no charge — they are NOT deflected by magnetic fields
3. In half-life problems, not distinguishing between “remaining” and “decayed”
4. Writing the wrong Q-value sign — check if reactants are heavier or lighter than products
5. Confusing fission and fusion: fission = splitting heavy nuclei, fusion = combining light nuclei

Priority Order for MDCAT: Radioactive decay types → Half-life and decay laws → Binding energy → Fission and fusion → Nuclear reactions

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