In a Rutherford scattering experiment when a projectile of charge $Z_1$ and mass $M_1$ approaches a target…

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 $\mathrm{M}_2$, the distance of closest approach is $\mathrm{r}_0$. The energy of the projectile is
  1. directly proportional to $\mathrm{M}_1 \times \mathrm{M}_2$
  2. directly proportional to $\mathrm{Z}_1 \mathrm{Z}_2$
  3. inversely proportional to $Z_1$
  4. directly proportional to mass $\mathrm{M}_1$

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 $\mathrm{z}_2$. At the distance of closest approach, the kinetic energy of particle is completely converted to potential energy. Mathematically, $\frac{1}{2} \mathrm{M}_1 \mathrm{u}^2=\frac{1}{4 \pi \varepsilon_0} \frac{\mathrm{z}_1 \mathrm{z}_2}{\mathrm{r}_0}$ So the energy of the particle is directly proportional to $\mathrm{z}_1 \mathrm{z}_2$.

Asked in: NEET 2009 (Screening)

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