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PC10 — Atomic & Nuclear Physics

📖 PC10 · CDS General Science — Physics 🎯 CDS Level : High Priority

Nuclear physics explores the innermost structure of matter — atoms, nuclei, and the immense energy locked within. CDS consistently tests atomic models, types of radioactive decay, half-life, and the distinction between nuclear fission and fusion. This chapter is scoring when studied systematically.

📌 CDS focuses on: Atomic models (Rutherford, Bohr); radioactivity — types (α, β, γ) and their properties; half-life concept; nuclear fission vs fusion; mass-energy equivalence E = mc²; applications (nuclear reactor, atomic bomb, hydrogen bomb, X-rays).

Topics at a Glance

① Atomic Models

Thomson, Rutherford, Bohr, quantum

② Radioactivity

α, β, γ decay — properties

③ Half-Life

Decay rate; amount remaining

④ Nuclear Fission

Heavy nucleus splits; chain reaction

⑤ Nuclear Fusion

Light nuclei combine; stars; H-bomb

⑥ X-rays & E=mc²

Properties; mass-energy equivalence

1. Atomic Models

1.1

Evolution of the Atomic Model

From plum pudding to quantum cloud — how our understanding evolved

Fig. 1 — Three landmark atomic models. Bohr's model (1913) was the first to successfully explain the hydrogen emission spectrum using quantised (fixed-energy) electron orbits.

Bohr's Postulates (key for CDS):
1. Electrons revolve in fixed circular orbits (shells) — specific allowed radii only.
2. While in these orbits, electrons do NOT emit radiation (no energy loss — stable orbits).
3. When an electron jumps from a higher orbit to a lower orbit, it emits a photon of energy = difference in energy levels: E = hf.
4. When a photon is absorbed, the electron jumps to a higher orbit.

2. Radioactivity

2.1

Alpha, Beta & Gamma Radiation — Properties & Penetration

Three very different forms of radiation from unstable nuclei

Fig. 2 — Penetrating and ionising power of the three radiations are inversely related. Alpha is the most ionising but least penetrating; gamma is least ionising but most penetrating.

Property	Alpha (α)	Beta (β)	Gamma (γ)
Nature	Helium nucleus (2p + 2n; charge +2)	Fast electron (charge −1)	Electromagnetic radiation (no charge, no mass)
Penetration	Least — stopped by paper or few cm air	Moderate — stopped by a few mm Al	Greatest — needs several cm of lead/concrete
Ionising power	Greatest (most dangerous to nearby tissue)	Moderate	Least (but penetrates deep into body)
Deflection in field	Deflected toward negative plate	Deflected toward positive plate (opposite to α)	Not deflected (no charge)
Speed	~0.1c (slowest)	Up to 0.9c	Speed of light c (fastest)

3. Half-Life

3.1

Radioactive Decay Rate

⚡ Half-Life Calculations

Half-life (T½): Time in which half the atoms in a radioactive sample decay. After n half-lives: Remaining amount = N₀ × (1/2)ⁿ = N₀ / 2ⁿ Examples: Initial amount: 80 g; T½ = 10 years After 10 yr: 40 g (n=1); After 20 yr: 20 g (n=2); After 30 yr: 10 g (n=3) If T½ = 5 years and initial amount = 160 g: After 20 years (= 4 half-lives): remaining = 160/2⁴ = 160/16 = 10 g Carbon dating: Carbon-14 has T½ ≈ 5730 years → used to date archaeological specimens up to ~50,000 years old.

4. Nuclear Fission vs Fusion

4.1

Two Ways to Release Nuclear Energy

⚡ Nuclear Fission

A heavy nucleus (e.g. Uranium-235 or Plutonium-239) splits into smaller nuclei when struck by a neutron
Produces 2-3 more neutrons → chain reaction possible
Releases enormous energy (from mass-energy conversion)
Atomic bomb (A-bomb): uncontrolled fission chain reaction
Nuclear reactor: controlled fission; used to generate electricity
Moderator (heavy water/graphite) slows neutrons; Control rods (cadmium) absorb neutrons

⚡ Nuclear Fusion

Light nuclei (hydrogen isotopes — deuterium + tritium) combine to form heavier nucleus (helium) + energy
Releases MORE energy per unit mass than fission
Requires extremely high temperature (~10⁷ to 10⁸ K) — "thermonuclear reaction"
Hydrogen bomb (H-bomb): uncontrolled fusion (triggered by fission bomb)
Sun's energy source: hydrogen nuclei fusing into helium continuously
Controlled fusion (ITER project): future clean energy goal

⚡ Mass-Energy Equivalence (E = mc²)

Einstein's equation: E = mc² E = energy released (Joules) m = mass converted (kg) c = speed of light = 3 × 10⁸ m/s In nuclear reactions, a tiny loss of mass (mass defect) results in enormous energy release. Even 1 gram of mass = 9 × 10¹³ J of energy. Mass defect: actual mass of nucleus < sum of masses of protons + neutrons Binding energy: energy needed to break the nucleus apart into constituents. Higher binding energy per nucleon → more stable nucleus. Iron-56 has highest binding energy per nucleon (most stable element).

⚠ Fission vs Fusion Traps: (1) Atomic bomb = fission (U-235 or Pu-239); Hydrogen bomb = fusion (triggered by fission). (2) Sun works by fusion — NOT fission. (3) Nuclear power plants use fission — NOT fusion (controlled fusion is not yet commercial). (4) Fusion releases MORE energy per unit mass than fission. (5) Moderator slows neutrons; control rod absorbs neutrons — different functions.

📝 CDS PYQ

Atomic & Nuclear Physics

Q1. The half-life of a radioactive substance is 10 years. Starting with 80 g, how much remains after 30 years?

(a) 40 g
(b) 20 g
(c) 10 g
(d) 5 g

Answer: (c) 10 g
30 years = 3 half-lives (30÷10=3). Remaining = 80 × (1/2)³ = 80/8 = 10 g. After each half-life: 80→40→20→10 g. This is the most frequently tested half-life type in CDS — always divide the total time by T½ to find n, then apply N₀/2ⁿ.

Q2. The energy produced in the Sun comes from:

(a) Nuclear fission
(b) Chemical combustion
(c) Nuclear fusion
(d) Radioactive decay

Answer: (c) Nuclear fusion
The Sun produces energy by the thermonuclear fusion of hydrogen nuclei (protons) forming helium nuclei. The enormous gravitational pressure at the Sun's core maintains the extreme temperatures (~15 million K) needed for fusion. This converts ~4 million tonnes of mass to energy per second via E = mc². Nuclear power plants use fission — the Sun uses fusion.

Q3. Which radiation cannot be deflected by electric or magnetic fields?

(a) Alpha
(b) Beta
(c) Gamma
(d) Both alpha and beta

Answer: (c) Gamma
Gamma radiation consists of electromagnetic waves — it has no charge and no mass. Since electric and magnetic fields act on charged particles, gamma rays are not deflected. Alpha particles (charge +2) deflect toward the negative plate; beta particles (charge −1) deflect toward the positive plate. Gamma rays travel straight through both electric and magnetic fields.

Q4. In a nuclear reactor, the function of the moderator (heavy water) is to:

(a) Absorb all neutrons to stop the reaction
(b) Slow down fast neutrons to thermal speeds
(c) Reflect neutrons back into the core
(d) Cool the reactor

Answer: (b) Slow down fast neutrons to thermal speeds
The moderator (heavy water D₂O, ordinary water H₂O, or graphite) slows down fast neutrons produced in fission so they can be captured by U-235 atoms to sustain the chain reaction. Slow (thermal) neutrons are more easily absorbed by U-235 than fast neutrons. Control rods (cadmium or boron) absorb neutrons to control the reaction rate — different from the moderator's function.

📚 Formula Sheet — PC10

⚡ Radioactivity

α = helium nucleus; +2 charge
β = electron; −1 charge
γ = EM wave; no charge, no mass
Penetration: γ > β > α
Ionising: α > β > γ

⏳ Half-Life

Remaining = N₀ / 2ⁿ
n = total time / T½
C-14: T½ = 5730 yr (dating)
U-238: T½ = 4.5 billion yr
Each half-life: amount halves

⚡ Fission vs Fusion

Fission: U-235 splits; A-bomb; reactors
Fusion: H-isotopes join; H-bomb; Sun
E = mc²; c = 3×10⁸ m/s
Moderator slows neutrons
Control rods absorb neutrons

🔬 Atomic Models

Thomson: plum pudding
Rutherford: nuclear (tiny +ve nucleus)
Bohr: fixed quantised orbits
Bohr: explained H spectrum
Quantum: electron cloud (modern)

⚡ Quick Revision — PC10

⚡ Radiation Summary

α: heaviest, most ionising, least penetrating
γ: massless, least ionising, most penetrating
α deflects to −ve plate; β to +ve plate
γ: not deflected by fields
All three stopped by: α=paper; β=Al; γ=lead

⏳ Half-Life

n half-lives → N₀/2ⁿ remaining
C-14 dating: up to 50,000 years
Decay is random but predictable statistically
T½ unchanged by temp/pressure/chemical state

🚨 CDS Traps

Sun = fusion (not fission)
Nuclear reactor = controlled fission
A-bomb = fission; H-bomb = fusion
Moderator ≠ control rod
Fusion releases more energy per kg than fission

📝 Practice Exercise

E-01

The half-life of a radioactive element is 5 years. If you start with 64 g, how much remains after 20 years?

(a) 8 g
(b) 4 g
(c) 16 g
(d) 2 g

E-02

Nuclear fission involves:

(a) Combining two light nuclei
(b) Splitting a heavy nucleus into lighter nuclei
(c) Emission of gamma rays only
(d) Conversion of neutrons into protons only

E-03

Which atomic model successfully explained the line spectrum of hydrogen?

(a) Thomson model
(b) Rutherford model
(c) Bohr model
(d) Dalton model

Answers: E-01: (b) 4 g [n = 20/5 = 4 half-lives; remaining = 64/2⁴ = 64/16 = 4 g] | E-02: (b) Splitting a heavy nucleus — fission; fusion combines light nuclei | E-03: (c) Bohr model — proposed quantised orbits, explaining H emission spectrum (Balmer series etc.)

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