Quick Summary
Atomic and nuclear physics covers the structure of atoms, radioactive decay, and nuclear energy. Weightage: 8–10 marks in TN HSE. This chapter has consistent presence in NEET (Bohr model, radioactive decay, nuclear reactions) and JEE (energy levels, mass defect).
Key Concepts and Definitions
- Atomic number (Z): Number of protons in nucleus
- Mass number (A): Total number of protons + neutrons
- Isotopes: Same Z, different A
- Binding energy: Energy required to completely separate all nucleons
- Mass defect (Δm): Difference between sum of individual nucleon masses and actual nuclear mass
- Half-life (T½): Time for half the radioactive nuclei to decay
Formulae
| Concept | Formula |
|---|---|
| Bohr's orbit radius | rn = n²a₀/Z (a₀ = 0.529 Å) |
| Bohr's energy level | En = −13.6 Z²/n² eV |
| Photon wavelength | 1/λ = RH(1/n₁² − 1/n₂²) |
| Mass-energy equivalence | E = Δmc² |
| Binding energy | BE = Δm × 931.5 MeV/u |
| Radioactive decay law | N = N₀ e^(−λt) |
| Activity | A = λN |
| Half-life | T½ = 0.693/λ |
| Mean life | τ = 1/λ = 1.44 T½ |
Bohr's Model of Hydrogen Atom
Postulates
1. Electrons move in circular orbits without emitting radiation (stationary states) 2. Angular momentum is quantised: mvr = nh/2π 3. Radiation is emitted/absorbed when electron jumps: E = hf = Ei − Ef
Results
- Radius of nth orbit: rn = (0.529 n²)/Z Å
- Velocity in nth orbit: vn = Ze²/(2ε₀nh)
- Energy of nth orbit: En = −13.6 Z²/n² eV
Energy of hydrogen ground state (n=1): −13.6 eV
Spectral series: Lyman (UV, n→1), Balmer (visible, n→2), Paschen (IR, n→3)
Nuclear Structure
Nuclear radius: R = R₀A^(1/3), R₀ = 1.2 × 10⁻¹⁵ m
Nuclear density: ≈ 2.3 × 10¹⁷ kg/m³ (enormous — same for all nuclei)
Mass defect: Δm = [Zmp + (A−Z)mn] − M_nucleus
Binding energy: BE = Δm × 931.5 MeV (if Δm in atomic mass units)
Binding energy per nucleon peaks at iron-56 (most stable nucleus)
Radioactivity
Three types of radioactive emissions:
| Type | Nature | Penetration | Ionising |
|---|---|---|---|
| Alpha (α) | ⁴He nucleus | Lowest (paper) | Highest |
| Beta (β) | Electron or positron | Medium (Al foil) | Medium |
| Gamma (γ) | EM radiation | Highest (lead) | Lowest |
Decay law: N(t) = N₀ e^(−λt)
Half-life: T½ = 0.693/λ
Activity: A = λN (SI unit: Becquerel; 1 Ci = 3.7 × 10¹⁰ disintegrations/s)
Nuclear Reactions
Fission: ²³⁵U + n → ⁹²Kr + ¹⁴¹Ba + 3n + energy (~200 MeV per fission)
- Chain reaction controlled in nuclear reactors (moderator slows neutrons)
- Critical mass needed for sustained chain reaction
Fusion: ²H + ³H → ⁴He + n + 17.6 MeV
- Requires extremely high temperature (~10⁷ K) — "thermonuclear reaction"
- Powers the Sun; basis of hydrogen bomb
Important Questions
One Mark
1. Write the energy of the electron in the ground state of hydrogen atom. 2. Define half-life of a radioactive substance. 3. What is mass defect? 4. Name the spectral series of hydrogen in the visible region. 5. What is nuclear fission?
Short Answer (3 marks)
1. State Bohr's postulates and derive the expression for the radius of nth orbit. 2. Explain alpha, beta, and gamma decays with examples. 3. Define binding energy and binding energy per nucleon. Explain the significance of the BE/A curve.
Long Answer (5 marks)
1. Explain Bohr's model of hydrogen atom. Derive the expression for the energy of the electron in nth orbit and find the wavelength of the spectral lines. 2. Explain radioactive decay law. Derive the expression for half-life and mean life. Calculate the activity of a given sample.
Board Exam Tips
- Bohr model numericals — always use En = −13.6/n² for hydrogen (Z=1)
- Radioactive decay problems: find N after n half-lives → N = N₀ × (1/2)ⁿ
- Nuclear reactions — balance mass number and atomic number on both sides
- "Why is nuclear density same for all nuclei?" — R ∝ A^(1/3), so volume ∝ A, density = constant
Revision Checklist
- [ ] State Bohr's postulates and derive radius formula
- [ ] Calculate energy levels and wavelengths of spectral series
- [ ] Explain mass defect and binding energy
- [ ] Draw and explain BE/A curve
- [ ] Explain and distinguish α, β, γ decay
- [ ] Apply radioactive decay law and half-life formula
- [ ] Explain nuclear fission and chain reaction
- [ ] Describe nuclear fusion and compare with fission
📚 Get Samacheer Kalvi 12th Physics Guide on Amazon