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. directly proportional to `Z_(1)Z_(2)`
C. inversely proportional to `Z_(1)`
D. directly proportional to mass `M_(1)`

Answer

B

Explanation

A particle of mass `M_(1)` and change `z_(1)` possesses initial velocity `u`, when it is at a large distance from the nucleus of an atom having atomic number `z_(2)`. At the distance of closed approach, the kinetic energy of particle is complately converted to potential energy. Mathematical,
`(1)/(2)M_(1)u^(2) = (1)/(4pi epsilon_(0)) (z_(1)z_(2))/(r_(0))`
So the energy of the particle is directly proportional to `z_(1)z_(2)`.