Question

The trajectory of a $\alpha $ particle is shown in figure below. Then, impact parameter is represented by:

A. a
B. b
C. c
D. d

Answer 1

Hint: A $\alpha $ particle is a nucleus atom consisting of two protons and two neutrons bound together identical with Helium $ - 4$ or sometimes denoted as $H{e^{2 + }}$ . When these alpha particles are bombarded with some kinetic energy towards the target nucleus, then the path followed by the alpha particles is called the trajectory of the alpha particle. We will examine the trajectory of alpha particles and various basic parameters which are used in physics for the trajectory of alpha particles.

Complete step by step answer:
When alpha particles are bombarded with some initial velocity, we observe the different trajectories followed by the alpha particle. The trajectory of an alpha particle depends upon the impact parameter. Impact parameter is the perpendicular distance between the initial velocity vector and the centre of the target nucleus.

So, from the given trajectory in the question diagram we can see that the perpendicular distance between the initial velocity vector and the centre of the Gold nucleus is denoted by ‘b’. So, the impact parameter of the alpha particle’s trajectory is represented by ‘b’.

Hence, the correct option is B.

Note: It should be remembered that, all the alpha particles when reaches near the targeted nucleus they gets deflected with some angle, and the impact parameter ‘b’ is inversely proportional to the initial kinetic energy of the alpha particles $b \propto \dfrac{1}{K}$ which shows, larger the velocity of alpha particle, lesser the impact parameter and less the kinetic energy more the impact parameter of the alpha particle.