(1) The distance of closet approach (rc) is given by the relation
where 1/2 mv2 is initial K.E of incident α–particle. It is obvious from the above relation that the radius of nucleus must be smaller than the calculated value of r c as an alpha particle cannot touch the periphery of the nucleus on account of strong repulsive force.
(2) Impact Parameter
Impact parameter is defined as the perpendicular distance of the initial velocity vector of the αparticle from the central line of the nucleus when the α–particle is far away from the nucleus of the atom as shown in Fig. (a).
Fig. (b) shows three α–particle 1, 2 and 3 fired towards the nucleus N. Impact parameter is leas for particle 1. The angle of scattering of 1 is more than that of 2 and 3. This is because particle 1 is coming more close to nucleus N and therefore experiences more replusive force.
It can be shown that the number of α–particle scattered through an angle , is
(1) directly proportional to thickness (t) of the gold foil.
(2) directly proportional to atomic number (z) of scattering nuclei.
(3) inversly proportional to kinetic energy (K) of incident α–particle.
(4) inversly proportional to sin4 (θ/2).
