Answer: b = Z e²/(4pi eps 0 × 2E) × cot(theta/2).
- A b = Z e²/(4pi eps<sub>0</sub> × 2E) × cot(theta/2)
- B b = h/(mv), the de Broglie wavelength formula for the alpha particle
- C b = a₀/n², the Bohr radius formula for an atomic orbit
- D b = r/theta, a simple ratio with no dependence on charge or energy
Correct answer: A. b = Z e²/(4pi eps<sub>0</sub> × 2E) × cot(theta/2)
Explanation: Rutherford scattering: b = (Z e²/4pi eps<sub>0</sub>) × cot(theta/2) / (2E<sub>kin</sub>). Larger b gives smaller deflection angle.
The Geiger–Marsden alpha-scattering result: a few alpha particles bounce back at large angles, which rules out Thomson’s diffuse model and demands a tiny, massive, positively charged nucleus. Image: Kurzon, CC BY 3.0, via Wikimedia Commons.
Concept context
Thomson's plum-pudding model, Rutherford's nuclear model from alpha-scattering, Bohr's postulates and hydrogen spectrum, spectral series (Lyman to Pfund), Rydberg formula, and limitations of each model.