Explain Rutherford's explanation for scattered `alpha`-particles.

Explanation

Rutherford suggested that since large number of a-particles are scattered at very small angles, atoms must be largely hollow.
Since the gold foil is very thin, it can be assumed that `alpha` particles will suffer not more than one scattering during their passage through it.
`alpha`-particles are nuclei of helium atoms and carry two + 2e charge and have the mass of the helium atom. For gold Z = 79, the nucleus of gold is about 50 times heavier than an a-particle it is assume that stationary throughout the scattering process.
Under these assumptions, the trajectory of an a-particle can be computed using Newton.s second law of motion and the Coulomb.s law for force of repulsion between the O-particle and the positively charged nucleus.
The magnitude of Coulomb.s repulsive force
`I^(2)=(1)/(4pi epsi_(0)) *((Ze)(2e))/(r^(2))`
wherer the distance between the c-particle and the nucleus and `epsi_(0)` is the permittivity of vacuum. The force is directed along the line joining the cparticle and the nucleus and varies continuously with the displacement of `alpha`-particle