Atoms is Chapter 12 of CBSE Class 12 Physics. This chapter traces the development of atomic models from Thomson’s plum pudding model to Rutherford’s nuclear model to Bohr’s model. You will learn Bohr’s postulates, energy levels of hydrogen atom, and spectral series.
This chapter carries 4–5 marks. Bohr’s postulates, energy level calculations, and hydrogen spectral series are most tested.
Key Concepts
1. Rutherford’s Nuclear Model
Alpha particle scattering experiment showed that the atom has a tiny, dense, positively charged nucleus at the centre, with electrons orbiting around it.
Limitation: An orbiting electron should continuously radiate energy and spiral into the nucleus — but atoms are stable. Classical physics couldn’t explain this.
2. Bohr’s Model of Hydrogen Atom
Postulates
- Electrons revolve in fixed circular orbits (stationary orbits) without radiating energy
- Quantisation: Angular momentum is quantised: L = mvr = nh/(2π), n = 1, 2, 3…
- Energy is emitted/absorbed only when an electron jumps between orbits: E = hν = E_i − E_f
Key Formulae for Hydrogen (Z = 1)
| Quantity | Formula |
|---|---|
| Radius of nth orbit | rn = 0.529 × n² Å (= n² × a₀, where a₀ = 0.529 Å) |
| Velocity in nth orbit | vn = 2.18 × 10⁶/n m/s |
| Energy of nth level | En = −13.6/n² eV |
Ground state (n=1): E = −13.6 eV; First excited (n=2): E = −3.4 eV
3. Hydrogen Spectral Series
1/λ = R(1/n₁² − 1/n₂²) where R = 1.097 × 10⁷ m⁻¹ (Rydberg constant)
| Series | Transition to n₁ | Region |
|---|---|---|
| Lyman | n₁ = 1 | Ultraviolet |
| Balmer | n₁ = 2 | Visible |
| Paschen | n₁ = 3 | Infrared |
| Brackett | n₁ = 4 | Infrared |
| Pfund | n₁ = 5 | Infrared |
Solved Examples
Example 1
Find the energy of the electron in the 3rd orbit of hydrogen.
Answer: E₃ = −13.6/3² = −13.6/9 = −1.51 eV
Example 2
Find the wavelength of the first line of the Balmer series (n₂ = 3 to n₁ = 2).
Answer: 1/λ = R(1/4 − 1/9) = R(9−4)/36 = 5R/36 = (5 × 1.097 × 10⁷)/36 = 1.524 × 10⁶
λ = 1/(1.524 × 10⁶) = 6.56 × 10⁻⁷ m = 656 nm (red light)
Quick Revision Points
- Bohr: quantised orbits, L = nh/(2π), En = −13.6/n² eV
- rn ∝ n²; vn ∝ 1/n; En ∝ −1/n²
- Ground state: n=1, E = −13.6 eV; ionisation energy = 13.6 eV
- Lyman (UV), Balmer (visible), Paschen/Brackett/Pfund (IR)
- 1/λ = R(1/n₁² − 1/n₂²)
Previous: Ch 11 — Dual Nature
Next: Ch 13 — Nuclei
Chapter Navigation
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Practice What You Learned
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