Q130 / 180 · KCET 2023 · Physics
In the Rutherford's alpha scattering experiment, as the impact parameter increases, the scattering angle of the alpha particle.
- Aremains the same
- Bis always $90^{\circ}$
- Correct answerCdecreases
- Dincreases
Solution
In the Rutherford's $\alpha$-scattering experiment,
impact parameter $(b)$ and scattering angle $\theta$ are related as,
$\begin{aligned} b & =\frac{1}{4 \pi \varepsilon_0} \cdot \frac{z e^2 \cot \frac{\theta}{2}}{\left(\frac{1}{2} m v^2\right)} \\ \Rightarrow \quad b & \propto \cot \frac{\theta}{2}\end{aligned}$
Thus, with the increase of impact parameter $(b)$, $\cot \frac{\theta}{2}$ increases. It is possible only when $\theta$ will decrease.
Hence, the correct answer is option: 'C'.