Atoms · Class 12 · CBSE · Science Physics

In the Rutherford scattering experiment, what is the relation between the impact parameter b and the scattering angle theta for a given initial veloc…

Practice question from Atoms (Class 12 · CBSE · Science Physics), with the correct answer and a step-by-step solution.

medium · MCQ · Q-0FE7CC

In the Rutherford scattering experiment, what is the relation between the impact parameter $b$ and the scattering angle $\theta$ for a given initial velocity of the $\alpha$ -particles?

A. $b$ is directly proportional to $\theta$
B. $b$ is inversely proportional to $\theta$
C. $b$ is directly proportional to $\cot(\theta/2)$ Correct answer
D. $b$ is directly proportional to $\tan(\theta/2)$

Solution

The impact parameter $b$ in alpha particle scattering is given by $b = \frac{Ze^2 \cot(\theta/2)}{4\pi \epsilon_0 \frac{1}{2}mv^2}$ , which shows that $b$ is directly proportional to $\cot(\theta/2)$ .

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