Last Updated: May 2026
CBSE Class 12 Physics Chapter 12 — Atoms covers Thomson’s, Rutherford’s and Bohr’s models of the atom, line spectra, hydrogen atom energy levels, and Bohr’s postulates. This is a high-yield CBSE board chapter — typical 5–8 marks combined across MCQs, Case Study questions, and 2-mark numericals. This guide gives complete NCERT-aligned notes plus 25 practice MCQs and important questions.
Chapter Overview
- NCERT Pages: 11.1 to 11.9 (~14 pages)
- Board exam weightage: 5–8 marks
- Topics: Atomic models, Rutherford’s experiment, Bohr’s theory, hydrogen spectrum, energy levels, ionisation energy
1. Thomson’s Plum Pudding Model (1898)
J.J. Thomson proposed that the atom is a uniform sphere of positive charge with electrons embedded in it like raisins in a pudding.
Failed because: couldn’t explain Rutherford’s α-scattering results.
2. Rutherford’s α-Scattering Experiment (1911)
Rutherford bombarded a thin gold foil with α-particles and observed:
- Most α-particles passed undeflected
- Some were deflected through small angles
- Very few (1 in 8000) bounced back at large angles
Conclusions
- Atom is mostly empty space
- Positive charge is concentrated at the centre — the nucleus
- Nucleus has a small radius (~10⁻¹⁵ m) compared to the atom (~10⁻¹⁰ m)
- Mass of atom is concentrated in the nucleus
Distance of Closest Approach
For an α-particle of kinetic energy K approaching a nucleus of atomic number Z:
r₀ = (1/4πε₀) × (2Ze²)/K
This gives an upper limit on the radius of the nucleus.
Impact Parameter
b = (1/4πε₀) × (Ze² cot(θ/2))/K
where θ is the scattering angle. Smaller impact parameter → larger deflection.
3. Drawback of Rutherford’s Model
According to classical electromagnetic theory, an accelerating charge (the orbiting electron) should continuously radiate energy → spiral inward → atom should collapse in 10⁻⁸ s. But atoms are stable. Hence Rutherford’s model couldn’t explain atomic stability.
4. Bohr’s Model of Hydrogen Atom (1913)
Bohr’s Three Postulates
- Quantised orbits: Electrons revolve only in certain stable orbits without radiating energy. These are called stationary states.
- Quantised angular momentum: L = mvr = nh/(2π), where n = 1, 2, 3, … is the principal quantum number.
- Quantised emission/absorption: Radiation occurs only when an electron jumps from a higher orbit (ni) to a lower orbit (nf): hν = Ei − Ef.
5. Bohr’s Formulae for Hydrogen Atom
| Quantity | Formula | Value (n=1) |
|---|---|---|
| Radius of n-th orbit | rn = (ε₀h²n²)/(πme²) = 0.53 × n² Å (for H) | 0.53 Å (Bohr radius) |
| Velocity in n-th orbit | vn = e²/(2ε₀nh) = c/(137n) | 2.18 × 10⁶ m/s |
| Energy in n-th orbit | En = −me⁴/(8ε₀²h²n²) = −13.6/n² eV | −13.6 eV (Ground state) |
| Frequency of revolution | fn = vn/(2πrn) | 6.6 × 10¹⁵ Hz |
6. Hydrogen Spectrum — Spectral Series
| Series | Discovered By | nf | ni | Region |
|---|---|---|---|---|
| Lyman | Theodore Lyman (1906) | 1 | 2, 3, 4, … | Ultraviolet |
| Balmer | J.J. Balmer (1885) | 2 | 3, 4, 5, … | Visible |
| Paschen | F. Paschen (1908) | 3 | 4, 5, 6, … | Infrared |
| Brackett | F. Brackett (1922) | 4 | 5, 6, 7, … | Infrared |
| Pfund | A.H. Pfund (1924) | 5 | 6, 7, 8, … | Far Infrared |
Rydberg Formula
1/λ = R(1/nf² − 1/ni²)
R = 1.097 × 10⁷ m⁻¹ (Rydberg constant)
7. Excitation Energy and Ionisation Energy
Excitation Energy = energy needed to raise electron from ground state to higher level. For H: E2 − E1 = (−3.4) − (−13.6) = 10.2 eV.
Ionisation Energy = energy required to remove electron from ground state to infinity. For H: 13.6 eV.
8. Limitations of Bohr’s Model
- Applicable only to hydrogen-like atoms (one electron systems: H, He⁺, Li²⁺)
- Doesn’t explain fine structure of spectral lines (Zeeman/Stark effect)
- Doesn’t explain intensities of spectral lines
- Violates Heisenberg’s uncertainty principle (specifying both position and orbit)
9. de Broglie’s Explanation of Bohr’s Quantisation
de Broglie proposed that electron has wave nature with wavelength λ = h/(mv). For a stable orbit, the circumference must contain an integer number of de Broglie wavelengths:
2πrn = nλ = nh/(mv)
This naturally gives Bohr’s angular momentum quantisation.
Important Numerical Problems for Boards
Q1. Calculate the radius of the third orbit of hydrogen atom.
Sol: r₃ = 0.53 × 9 = 4.77 Å
Q2. Find the wavelength of the second Balmer line (n=4 → n=2).
Sol: 1/λ = 1.097 × 10⁷ × (1/4 − 1/16) = 1.097 × 10⁷ × 3/16. λ = 486 nm.
Q3. What is the ionisation energy of He⁺?
Sol: E = −13.6 × Z²/n² = −13.6 × 4/1 = −54.4 eV. So ionisation energy = 54.4 eV.
25 Practice MCQs
Quiz data missing.
FAQ
Q1. How many marks does this chapter carry in CBSE Class 12 Physics?
5–8 marks combined — usually 1 MCQ (1 mark), 1 Case Study (3-4 marks), 1 short answer (2-3 marks).
Q2. Are Bohr’s postulates required to be memorised verbatim?
Yes — board examiners look for the exact phrasing. Memorise word-for-word.
Q3. Is the Rydberg formula commonly tested?
Yes — direct numerical questions on spectral series wavelengths come almost every year.
Q4. Should I derive Bohr’s radius?
Derivation may be asked as a 5-mark question. Practice the full derivation including kinetic energy + potential energy + total energy steps.
Q5. What’s the fastest way to remember spectral series?
Mnemonic: Lyman (UV) — nf=1 — “L for Light Just Below visible”. Balmer (Visible) — nf=2. Paschen, Brackett, Pfund — IR with increasing nf.
