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(A) In a Rutherford scattering experiment,at the distance of closest approach $(r_0)$,the entire initial kinetic energy $(K)$ of the projectile is con

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directly proportional to $Z_1 Z_2$

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(A) In a Rutherford scattering experiment,at the distance of closest approach $(r_0)$,the entire initial kinetic energy $(K)$ of the projectile is converted into electrostatic potential energy $(U)$.The electrostatic potential energy is given by the formula:$U = \frac{1}{4 \pi \varepsilon_0} \frac{(Z_1 e)(Z_2 e)}{r_0}$Since the kinetic energy $K$ is equal to the potential energy $U$ at the point of closest approach:$K = \frac{1}{4 \pi \varepsilon_0} \frac{Z_1 Z_2 e^2}{r_0}$From this expression,it is clear that the energy of the projectile is directly proportional to the product of the charges of the projectile and the target nucleus,i.e.,$K \propto Z_1 Z_2$.

In a Rutherford scattering experiment,when a projectile of charge $Z_1$ and mass $M_1$ approaches a target nucleus of charge $Z_2$ and mass $M_2$,the distance of closest approach is $r_0$. The energy of the projectile is:

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