CBSE Class 12 · Physics · NCERT Physics Part-II
Atoms: chapter on a page
A cut of Shishya's notes for this chapter: the first paragraph of the introduction and the key ideas, formulas and facts, common mistakes and quick revision lists, word for word. Nothing is added or reworded; the worked examples are left out (they are on the chapter page).
About the notes: Written by Shishya's AI on 27 Sept 2026 from the chapter's title and class level, in Shishya's own words — not a copy or summary of the textbook. Read the official chapter for the book's own text, activities and exercises.
Fact-checked on 21 Oct 2026: an AI-assisted check of this note against cited sources; the errors it found were corrected that day. Some errors may remain.
Mind map
Drawn from the same notes by a fixed rule (no AI): each label is the item's own words — its bold term, its label before a colon, a short formula as written, or its first words.
The mind map as a list
- Key ideas
- Thomson's model (plum-pudding model)
- Rutherford's nuclear model
- Impact parameter and scattering angle
- Bohr's postulates (hydrogen atom)
- Electrons move in circular orbits…
- Only orbits for which angular…
- An electron in an allowed orbit does…
- Formulas and facts
- Bohr radius
- Radius of nth orbit
- Velocity in nth orbit
- Total energy of nth level
- Rydberg formula for wavelengths
- Frequency of emitted photon
- Kinetic and potential energy in orbit
- Worked examples
- Radius and speed of an electron in…
- Wavelength of the first Balmer line
- Energy required to ionise hydrogen…
- Watch out for
- Using positive energy values for…
- Confusing impact parameter with…
- Applying Bohr's formula directly to…
- Forgetting to square n in the energy…
- Mixing up emission and absorption
What this chapter is about
This chapter traces how scientists uncovered the structure of atoms. You begin with early ideas such as Thomson's model, then move to Rutherford's alpha-particle scattering experiment that revealed the tiny, dense, positively charged nucleus. The failure of classical physics to explain atomic stability and discrete spectral lines leads you to Bohr's model of the hydrogen atom, which introduces quantised orbits and energy levels.
Key ideas
- Thomson's model (plum-pudding model): Positive charge is spread uniformly through a sphere and electrons are embedded like plums in a pudding. This model could not explain large-angle scattering of alpha particles.
- Rutherford's nuclear model: Alpha particles fired at thin gold foil showed that most pass straight through, a few deflect at large angles, and very few bounce back. Conclusion: almost all atomic mass and all positive charge sit in a nucleus far smaller than the atom itself (radius ≈ 10⁻¹⁵ m versus atomic radius ≈ 10⁻¹⁰ m).
- Impact parameter and scattering angle: A smaller impact parameter (distance of approach to nucleus) gives a larger scattering angle. The relation involves cot(θ/2).
- Bohr's postulates (hydrogen atom):
- Electrons move in circular orbits around the nucleus under electrostatic attraction.
- Only orbits for which angular momentum L = n h/(2π), with n = 1, 2, 3 …, are allowed (quantisation of angular momentum).
- An electron in an allowed orbit does not radiate energy; energy is emitted or absorbed only when it jumps between orbits, with ΔE = h ν.
- Bohr radius and energy levels: The radius of the nth orbit is rₙ = n² a₀, where a₀ ≈ 0.529 Å. Energy Eₙ = −13.6/n² eV. Negative energy means the electron is bound.
- Hydrogen spectrum: Transitions from higher to lower levels emit photons whose wavelengths satisfy 1/λ = R (1/n₁² − 1/n₂²), with Rydberg constant R ≈ 1.097 × 10⁷ m⁻¹. Different series arise for different final levels n₁ (Lyman → 1, Balmer → 2, Paschen → 3, etc.).
- Limitations of Bohr model: It works well for hydrogen and hydrogen-like ions but cannot explain spectra of multi-electron atoms, fine structure, or the Zeeman effect without further modification.
Formulas and facts to remember
- Bohr radius: a₀ = ε₀ h² / (π m e²) ≈ 5.29 × 10⁻¹¹ m.
- Radius of nth orbit: rₙ = n² a₀ / Z (Z = atomic number; for hydrogen Z = 1).
- Velocity in nth orbit: vₙ = (Z e²) / (2 ε₀ n h) = (c α Z) / n, where α ≈ 1/137 is the fine-structure constant.
- Total energy of nth level: Eₙ = −(m e⁴ Z²) / (8 ε₀² h² n²) = −13.6 Z² / n² eV.
- Rydberg formula for wavelengths: 1/λ = R Z² (1/n₁² − 1/n₂²), n₂ > n₁.
- Frequency of emitted photon: ν = (Eₙ₂ − Eₙ₁) / h.
- Kinetic and potential energy in orbit: K = −E (positive), U = 2 E (negative), so total E = K + U = −K.
- Distance of closest approach (α-particle): d = 2 k Z e² / (½ m v²), giving nuclear size upper limit.
Common mistakes
- Using positive energy values for bound states → Remember energies are negative; the electron is bound.
- Confusing impact parameter with scattering angle (thinking larger impact parameter gives larger deflection) → Larger impact parameter means weaker deflection.
- Applying Bohr's formula directly to multi-electron atoms → Bohr model is accurate only for one-electron systems (H, He⁺, Li²⁺, etc.).
- Forgetting to square n in the energy or radius formulas → rₙ ∝ n² and Eₙ ∝ 1/n².
- Mixing up emission and absorption: using n₂ < n₁ for emission → For emission n₂ > n₁; electron falls from higher to lower orbit.
Quick revision
- Rutherford's experiment proved the nucleus is tiny, dense and positively charged.
- Bohr's quantisation condition: L = n h/(2π).
- Energy levels: Eₙ = −13.6/n² eV for hydrogen.
- Rydberg formula: 1/λ = R (1/n₁² − 1/n₂²).
- Kinetic energy = −(total energy); potential energy = 2 × (total energy).
- Bohr model fails for atoms with more than one electron.