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Atoms
Physics · Class 12 · Part 2NCERT pp. 290–3022 sets × 25 questionsFree
Key facts and formulas for Atoms, three worked sample questions, and two full practice sets. Every question has a hint, a reason for every option and a step-by-step solution, with a calculator or animation where one helps. English and Hinglish.
Formula sheet for this chapter
| Idea | Rule or fact |
|---|
| Bohr radius | r = n² a₀ / Z, with a₀ = 0.53 Å |
| Bohr energy | E = −13.6 Z² / n² eV; K = −E, U = 2E |
| Bohr speed and period | v = 2.2 × 10⁶ × Z / n m/s; T ∝ n³ (frequency ∝ 1/n³) |
| Angular momentum | L = n h / 2π, with h/2π = 1.055 × 10⁻³⁴ J s |
| Spectral lines | 1/λ = R Z² (1/n_f² − 1/n²), R = 1.097 × 10⁷ m⁻¹; λ (nm) = 1240 / E (eV) |
| Series | Lyman n_f = 1, Balmer 2, Paschen 3, Brackett 4, Pfund 5; limit λ = n_f² / R |
| Number of lines | N = n (n − 1) / 2 for a large sample; a single atom gives at most n − 1 photons |
| Closest approach | d = 2Ze² / (4πε₀ K), e²/4πε₀ = 1.44 MeV fm; b = (d/2) cot(θ/2) |
| Rutherford scattering | N(θ) ∝ 1 / sin⁴(θ/2); about 1 in 8000 turns more than 90° |
| Absorption rule | A photon is absorbed only if its energy equals a gap exactly; an electron can give part of its energy |
Three sample questions
Q1. Read the statements about Thomson’s atom model. I. Positive charge is spread uniformly through the atom. II. Electrons are embedded in it like seeds in a watermelon. III. All the positive charge is at the centre. Which are correct?
- I and II only
- II and III only
- I and III only
- I, II and III
Hint and solution
Hint: One of the three statements describes the nuclear model of a different scientist. Find which one.
- Thomson: uniform positive sphere + embedded electrons — Thomson pictured a uniformly positive sphere with electrons stuck in it like seeds in a watermelon. So I and II are true.
- Rutherford: positive charge in a tiny nucleus — Charge concentrated at the centre is the nuclear model of Rutherford, not Thomson.
- I and II only — So only statements I and II are correct for Thomson. Option A.
Answer: A. Statement III describes Rutherford’s nuclear model, not Thomson’s.
Q2. Which statement about the alpha-particle scattering experiment is correct?
- Most particles are turned through more than 1°
- About 1 in 8000 particles turns through more than 90°
- About 14 percent turn by more than 1°
- Every particle passes straight through
Hint and solution
Hint: Recall the two numbers from Geiger and Marsden: the tiny fraction that deflect by a small angle and the far tinier fraction that bounce back.
- Most go nearly straight — Most alpha particles pass through the gold foil with almost no deviation. This removes options A and D.
- About 0.14 % deflect by more than 1° — Only about 0.14 percent turn by more than 1 degree, not 14 percent. This removes option C.
- About 1 in 8000 turn by more than 90° — Roughly one in eight thousand rebounds through more than 90 degrees. So the answer is the statement about 1 in 8000. Option B.
Answer: B. About 0.14 percent turn by more than 1°, and about 1 in 8000 by more than 90°; most go straight on.
Q3. Assertion A: Most alpha particles pass through a thin gold foil without deviation. Reason R: The atom is mostly empty space, with the positive charge in a tiny nucleus.
- Both A and R are true and R is the correct explanation of A
- Both A and R are true but R is not the correct explanation of A
- A is true but R is false
- A is false but R is true
Hint and solution
Hint: Ask whether R explains why most particles are undisturbed.
- Assertion: most particles go straight — This is the observed result: most alpha particles pass through with no deviation.
- Reason: atom mostly empty, tiny nucleus — The nucleus is about 10⁻⁴ times the atom in size, so the atom is mostly empty. This is also true.
- R explains A — Because the nucleus is so small, very few particles pass near it, so most feel no force. R is the correct explanation. Option A.
Answer: A. A tiny nucleus in a mostly empty atom means most particles never pass near it, so they go straight.
How to use this chapter
Read the NCERT pages first, then attempt Set 1 without the hints. Note every wrong answer in a mistake list, read the reason for each option, and retry Set 2 two days later. A topic is solid when you can say why each wrong option is wrong.