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Atoms

NCERT Class 12 Physics Chapter 12

Atoms for Class 12 Physics, JEE and NEET: alpha-particle scattering, Rutherford’s nuclear model, the Bohr model, energy levels and the hydrogen spectrum.

5 topics Updated 8 Nov 2026

For: Class 12, JEE and NEET

In the syllabus: JEE Class 12 syllabus, NEET Class 12 syllabus

With your textbook

NCERT Physics Part II (Class 12), Chapter 12 “Atoms”, reprint 2026-27.

Open the official NCERT chapter (PDF, 2.1 MB, ncert.nic.in)

Checked on 19 Oct 2026.

Learn in this order

  1. Alpha-particle scattering and Rutherford’s nuclear model

    Alpha-particle scattering experiment, impact parameter, distance of closest approach and solved examples.

    NCERT Sections 12.1–12.2 18 min read 4 solved examples 8 practice questions

  2. Atomic spectra

    Emission and absorption spectra, line vs continuous spectrum, hydrogen’s visible lines and solved examples.

    NCERT Section 12.3 11 min read 4 solved examples 7 practice questions

  3. Bohr model of the hydrogen atom

    Three postulates, radius r = na, energy −13.6/n eV, energy levels, ionisation energy and solved examples.

    NCERT Section 12.4 15 min read 4 solved examples 8 practice questions

  4. The line spectra of the hydrogen atom

    hν = Ei − Ef, Lyman, Balmer and Paschen series, the Rydberg formula, number of lines and solved examples.

    NCERT Section 12.5 13 min read 4 solved examples 8 practice questions

  5. De Broglie’s explanation of Bohr’s second postulate

    De Broglie’s standing electron waves, 2πr = nλ, L = nh/2π and the limitations of the Bohr model.

    NCERT Section 12.6 12 min read 4 solved examples 7 practice questions

Key formulas in this chapter

Rutherford’s nuclear model

  • F = (1/4πε)(2e)(Ze)/r
  • d = 2Ze/(4πεK)
  • b = (d/2) cot(θ/2)
  • r = e/(4πεmv)
  • K = e/(8πεr), U = −e/(4πεr)
  • E = −e/(8πεr)

Atomic spectra

  • 1/λ = R(1/2 − 1/n)
  • E = hν = hc/λ

Bohr model

  • L = mvr = nh/2π
  • hν = Ei − Ef
  • rn = n2 h2 ε0/(π m e2) = n2 a0
  • vn = e2/(2 ε0 n h)
  • En = −m e4/(8 n2 ε0^2 h2) = −13.6/n2 eV

Line spectra of hydrogen

  • hν = Ei − Ef
  • En = −13.6/n2 eV
  • hν = 13.6 (1/nf^2 − 1/ni^2) eV
  • 1/λ = R(1/nf^2 − 1/ni^2)
  • R ≈ 1.097 × 107 m−1
  • Ei + hν = Ef

De Broglie and Bohr’s postulate

  • 2πrn = nλ
  • λ = h/(m vn)
  • m vn rn = nh/2π
  • λn = 2πn a0

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