Q: In a Rutherford scattering experiment when a projectile of z1 and mass M1 approaches a target nucleus of charge z2 and mass M2. The distance of closest approach is r_{0} . The energy of the projectile is

(a) Directly proportional to M_{1} × M_{2}

(b) Directly proportional to z_{1}z_{2}

(c) Inversely proportional to z_{1}

(d) Directly proportional to mass M_{1}

Ans: (b)

Sol: $\large \frac{1}{2}M_1 v^2 = \frac{1}{4\pi \epsilon_0} \frac{(Z_1 e)(Z_2 e)}{r_0}$

Where r_{0} = distance of closest approach

$\large r_0 = \frac{1}{4\pi \epsilon_0} \frac{(Z_1 e)(Z_2 e)}{\frac{1}{2}M_1 v^2}$