In a Rutherford scattering experiment when a projectile of change `Z_(1)` and mass `M_(1)` approaches s target nucleus of change `Z_(2)` and mass `M_(2)`, te distance of closed approach is `r_(0)`. The energy of the projectile is

Options

A. Directly proportional to `M_1 xx M_2`
B. Inversely proportional to `M_1M_2`
C. Directly proportional to `Z_1Z_2`
D. Inversely proportional to `Z_1Z_2`

Answer

C

Explanation

In Rutherford's scattering experiment , the K.E. of the bombarding particle is completely converted into potential energy, when it is the distance of closest approach `(r_0)` .
`therefore 1/2M_1u^2 = (1)/(4piepsi_0) ((Z_1e)(Z_2e))/(r_0)`
`=(1)/(4piepsi_0) (e^2)/(r_0) (Z_1Z_2) = KZ_1Z_2`
Where `K=(1)/(4piepsi_0) (e^2)/(r_0)`
`therefore` The energy is directly propotional to `Z_1Z_2`