Atoms Ques 1
1. In a Rutherford scattering experiment when a projectile of charge $\mathrm{Z}_1$ and mass $\mathrm{M}_1$ approaches a target nucleus of charge $\mathrm{Z}_2$ and mass $\mathrm{M}_2$, the distance of closest approach is $r_0$. The energy of the projectile is
[2009]
(a) directly proportional to $\mathrm{Z}_1 \mathrm{Z}_2$
(b) inversely proportional to $\mathrm{Z}_1$
(c) directly proportional to mass $\mathrm{M}_1$
(d) directly proportional to $\mathrm{M}_1 \times \mathrm{M}_2$
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Answer:
Correct Answer: 1.(a)
Solution: (a) The kinetic energy of the projectile is given by
$ \begin{aligned} & \frac{1}{2} \mathrm{mv}^2=\frac{\mathrm{Ze}(2 \mathrm{e})}{4 \pi \varepsilon_0 \mathrm{r}_0} \\ & =\frac{\mathrm{Z}_1 \mathrm{Z}_2}{4 \pi \varepsilon_0 \mathrm{r}_0} \end{aligned} $
Thus energy of the projectile is directly proportional to $Z_1 Z_2$.
BETA
