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Question 27

In the Rutherford experiment, $$\alpha$$-particles are scattered from a nucleus as shown. Out of the four paths, which path is not possible?

image

Solution

Using Coulomb's law: $$\vec{F} = \frac{1}{4\pi\varepsilon_0}\frac{q_1 q_2}{r^2}\hat{r}$$

Given: $$q_1 = +2e$$, $$q_2 = +Ze$$

$$\vec{F} \propto \frac{(+2e)(+Ze)}{r^2}\hat{r} \quad (\text{Repulsive force})$$

Condition for path validity: trajectory must bend away from the nucleus.

Path C bends towards the nucleus, implying attraction.

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