In a Rutherford scattering experiment when a projectile of charge $Z_1$ and mass $M_1$ approaches a target…
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 $\mathrm{M}_2$, the distance of closest approach is $\mathrm{r}_0$. The energy of the projectile is
directly proportional to $\mathrm{M}_1 \times \mathrm{M}_2$
directly proportional to $\mathrm{Z}_1 \mathrm{Z}_2$
inversely proportional to $Z_1$
directly proportional to mass $\mathrm{M}_1$
Solution
A particle of mass $M_1$ and charge $z_1$ possess initial velocity $u$, when it is at a large distance from the nucleus of an atom having atomic number $\mathrm{z}_2$. At the distance of closest approach, the kinetic energy of particle is completely converted to potential energy. Mathematically,
$\frac{1}{2} \mathrm{M}_1 \mathrm{u}^2=\frac{1}{4 \pi \varepsilon_0} \frac{\mathrm{z}_1 \mathrm{z}_2}{\mathrm{r}_0}$
So the energy of the particle is directly proportional to $\mathrm{z}_1 \mathrm{z}_2$.