Question

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 to closest approached is $r_0$. The energy of the projectile is

• A. directly proportional to $M_1\times M_2$
• B. directly proportional to $Z_1{Z}_2$
• C. directly proportional to to $Z_1$
• D. directly proportional to mass $M_1$

Answer 1

Answer: (B)

directly proportional to $Z_1{Z}_2$

The particle of mass $M_1$ and charge $Z_1$ possess initial velocity $u$ when it at a large distance from the nucleus of an atom having atomic number $Z_2$. At the distance of closest approach, the kinetic energy of the particle is completely converted to potential energy.

$\frac{1}{2}{M}_1{u}^2=\frac{1}{4\pi {\epsilon }_0}\frac{Z_1{Z}_2}{r_0}$

So the energy of the particle is directly proportional to $Z_1{Z}_2$