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 of closest approach 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.
inversely proportional to $${Z_1}$$
D.
directly proportional to mass $${M_1}$$
Answer :
directly proportional to $${Z_1}{Z_2}$$
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 $${Z_2}.$$ At the distance of closest approach, the kinetic energy of particle is completely converted to potential energy. Mathematically,
$$\frac{1}{2}{M_1}{u^2} = \frac{1}{{4\pi {\varepsilon _0}}}\frac{{{Z_1}{Z_2}}}{{{r_0}}}$$
So, the energy of the particle is directly proportional to $${Z_1}{Z_2}.$$