Alpha Trajectory & Closest Approach Challenge
25 NEET-standard questions on the alpha-particle trajectory, impact parameter and scattering angle, the distance of closest approach from energy conservation, and the problems with electron orbits in the Rutherford model. Answer each one. If you get it wrong, Vidya Ma’am explains it with an animated movie you can control, a slider to play with, and a step-by-step solution. Then try again.
NCERT Physics XII Part II · Ch. 12 · pp. 293–295Keys: A–D or 1–4 to answer
🧠 Formula memory tricks (open before you start)
Impact parameterSmall b → large θ. Head-on: b minimum, θ ≈ 180°. Large b: θ ≈ 0.
Closest approachK = (1/4πε₀)(2e)(Ze)/r₀r₀ = 2Ze²/(4πε₀K) ∝ Z/K
Gold, 7.7 MeVr₀ ≈ 3.0×10⁻¹⁴ m = 30 fmactual nuclear radius ≈ 6 fm: the alpha never touches
Quick numberr₀ ≈ 2.88 Z / K(MeV) fm5.5 MeV on gold: 41 fm
Coulomb lawF = (1/4πε₀)(2e)(Ze)/r²halve r → 4 times F; energy U ∝ 1/r
Size of atomAtom ≈ 10⁻¹⁰ m; nucleus 10⁻¹⁵ to 10⁻¹⁴ mratio 10⁴ to 10⁵: mostly empty space
Electron orbite²/(4πε₀r²) = mv²/raccelerated charge radiates → spiral, continuous spectrum (but atoms show lines)
right first tryfixed after explanationstill to fix
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