CBSE Class 12 Physics Atoms PYQs Analysis (2021-2025)

Based on detailed analysis of last 5 years' papers. Perfect for 2026 Boards prep!

Key Trends

Weightage Breakdown: 1-2 MCQs/assertion-reason (1 mark), 1-2 short answers (2 marks), 1-2 numericals/derivations on Bohr model & spectrum (3-5 marks).
Repeated Topics: Bohr’s model (postulates, radius r_n = n² h² ε₀ / (π m e²), velocity v_n = e² / (2 ε₀ n h), energy E_n = -13.6 / n² eV), hydrogen spectrum (Lyman, Balmer, Paschen series), Rydberg formula, spectral lines calculation, de Broglie explanation of Bohr orbits, alpha particle scattering (impact parameter, distance of closest approach), limitations of Rutherford model.
Difficulty: Medium; Bohr model numericals (energy difference, wavelength) & Rydberg formula are most repeated & scoring.
Changes: More numericals on transition wavelength & energy levels in 2023–2025.

Most Important and Repeated Questions

Question Example	Type/Marks	Years Repeated	Notes
State Bohr’s postulates. Derive expression for radius, velocity & total energy of electron in nth orbit of hydrogen atom.	Derivation (4 marks)	2021, 2022, 2023, 2024, 2025	Repeated 5x; m v r = n h/(2π), centripetal = electrostatic → r_n = n² h² ε₀ / (π m e²), v_n = e² / (2 ε₀ n h), E_n = - (13.6 / n²) eV.
Using Rydberg formula, find wavelength of spectral line when electron jumps from n₂ to n₁ in hydrogen (or calculate energy difference).	Numerical (3 marks)	2021 Term 2, 2022, 2023, 2024	Repeated 4x; 1/λ = R (1/n₁² - 1/n₂²); R = 1.097 × 10⁷ m⁻¹; ΔE = 13.6 (1/n₁² - 1/n₂²) eV → λ = hc/ΔE.
Explain limitations of Rutherford model & how Bohr’s model overcomes them. Also explain de Broglie’s hypothesis for stationary orbits.	Short Answer/Theory (3 marks)	2022, 2023, 2024, 2025	Repeated 4x; Rutherford: no stability, no discrete spectrum; Bohr: angular momentum quantised → stable orbits; de Broglie: 2πr = nλ → mvr = n h/(2π).
Assertion: Energy of electron in Bohr orbit is negative. Reason: Electron is bound to nucleus (potential energy negative & larger in magnitude than kinetic).	Assertion-Reason (1 mark)	2023, 2024, 2025	Repeated 3x; Both true, reason explains (E = K + U = (1/2)mv² - kZe²/r = -kZe²/(2r)).
Calculate energy released when electron jumps from n=3 to n=2 in hydrogen atom (Balmer series).	Numerical (2-3 marks)	2021 Term 1, 2022, 2023, 2025	Repeated 4x; ΔE = 13.6 (1/2² - 1/3²) = 1.89 eV; λ = 656 nm (H-alpha line).
Find impact parameter b & distance of closest approach d in Rutherford alpha scattering for given scattering angle θ.	Numerical (3 marks)	2022, 2024	Repeated 2x; b = (Z₁ Z₂ e² / (4πε₀ K)) cot(θ/2), d = (Z₁ Z₂ e² / (4πε₀ K)) (1 + csc(θ/2)).
MCQ: The ratio of kinetic energy to potential energy in Bohr orbit is: (a) 1/2 (b) -1/2 (c) 1 (d) -1	MCQ (1 mark)	2021 Term 1, 2023, 2024	Repeated 3x; Answer (b) -1/2 (K = -E, U = 2E, K/U = -1/2).
Explain spectral series of hydrogen atom (Lyman, Balmer, Paschen, Brackett, Pfund). Mention region & transition.	Short Answer (3 marks)	2023, 2025	Repeated 2x; Lyman (UV, n₂→1), Balmer (visible, n₂→2), Paschen (IR, n₂→3), etc.
Case-based: Given transition n₂ → n₁, find wavelength, energy difference, or series name.	Case-Based (4 marks)	2023, 2025	Repeated 2x; Use Rydberg or energy formula.
Find ratio of de Broglie wavelength of electron in n=1 & n=2 orbits.	Short Answer (2 marks)	2021 Term 2, 2024	Repeated 2x; v₁/v₂ = 2/1 → λ₁/λ₂ = 1/2 (since λ ∝ 1/v).

Best Format for Preparation and Answering

Study Format: Memorize Bohr’s formulas (r_n, v_n, E_n) & Rydberg constant. Practice numericals on wavelength/energy difference daily. Make table for spectral series (region, transition, wavelength range).
Answer Format: Derivations: Use centripetal = electrostatic + angular momentum quantisation → solve for r, v, E. Numericals: Use E = -13.6/n² → ΔE = hc/λ. Always mention series name & region.
Tips: Bohr model derivations (radius, energy) & Rydberg formula numericals (transition wavelength) are highest repeat & marks. Learn limitations & de Broglie justification. Time: 8–10 mins for 3–5 mark questions. Very scoring with correct sign & units.

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