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Statement 1: Experiments show that the distance of closest approach to a gold nucleus for an alpha particle of kinetic energy 5.5 MeV is about 4 * 10^(-14) m. Statement 2: In Rutherford's scattering calculations, both the Coulombic repulsion force and the short-range nuclear force are taken into account.

1. Statement 1 is true; Statement 2 is true; Statement 2 is the correct explanation of Statement 1.
2. Statement 1 is true; Statement 2 is true; Statement 2 is NOT the correct explanation of Statement 1.
3. Statement 1 is true; Statement 2 is false.
4. Statement 1 is false; Statement 2 is true.

Correct answer: Statement 1 is true; Statement 2 is false.

Solution

Statement 1 is TRUE: using energy conservation, at closest approach all kinetic energy converts to electrostatic PE: KE = k*q1*q2/r. For alpha (Z=2) and gold (Z=79): r = k*(2e)*(79e)/KE = (9e9 * 2 * 79 * (1.6e-19)²)/(5.5*1.6e-13) ~ 4e-14 m. Statement 2 is FALSE: Rutherford's classical model uses only Coulombic repulsion. Short-range nuclear forces act at distances much smaller than 4e-14 m and are NOT included in his original scattering theory.

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