Question

In scattering, the impact parameter $b$ is defined as the:

Answer 1

Impact Parameter

1. The scattering of an $\alpha$-particle from a nucleus depends on its distance of closest approach to the nucleus or on an equivalent length, called the impact parameter $\text{'}b\text{'}$.
2. The impact parameter is defined as the perpendicular distance of the velocity vector of the $\alpha$-particle from the centre of the nucleus, when it is far away from the atom.
3. For large impact parameters, the repulsive force experienced by the $\alpha$-particle is weak (because of its inverse square law character) and the $\alpha$-particle passes almost undeflected.
4. For small impact parameter, the repulsive force is large and so the $\alpha$-particle is scattered through large angle.
5. For a head-on collision, when the $\alpha$-particle just aims at the centre of the nucleus, the impact parameter $b=0$, scattering angle $\theta =180°$, ie, the $\alpha$-particle is reversed back along its original path.
6. Thus the shape of the trajectory of the scattered $\alpha$-particles depends on the impact parameter and the nature of the potential field.