Show the trajectory of a particle of different impact parameter and using it how did Rutherford determine the upper limit of the nuclear size ?

Explanation

Impact parameter is the perpendicular distance of the initial velocity vector of the a-particle from the centre of the nucleus and the trajectory of the `alpha`-particle depend on the impact parameter of collision b with the nucleus.
A given beam of a particles has a distribution of impact parameter b, so that the beam is scattered in various directions with different probabilities. In a beam all particles have nearly same kinetic energy.

The smaller the impact parameter b of the C-particle the closer it is to the nucleus and its scattering is larger means the angle of scattering is larger.
In case of head on collision, the impact parameter is minimum (b = 0) and the C-particle rebounds back `(theta=pi)`.
As the impact parameter of the `alpha`-particle becomes larger, the scattering angle decreases and a particle for a larger impact parameter keeps the motion on its original trajectory without scattering that is scattering angle `theta=0^(@)`.
Hence, only a small fraction of the number of incident particles rebound back indicates that the number of `alpha`-particles undergoing head on collision is small. This means that the mass of the atom is concentrated in a small volume. Therefore, Rutherford scattering is a powerful way to determine an upper limit to the size of the nucleus.
From this experiment, Rutherford suggested the dimension of nucleus is `10^(-15)m` to `10^(-14)m`