Rutherfords Scattering Formula for a-rays

According to Rutherford, the nucleus of an atom (with charge Ze) and an a-particle (with charge E and 

Further, we have the theorem of the conservation of angular momentum, in virtue of which 

Substituting this value in the above equation and carrying out a few transformations, we have 

This gives tlie angle of deviation as a function of 6, the distance of tlie rectilinear prolongation of the path, of the a-particle (the asymptote) from the nucleus. 

It is now easy to calculate how many a-particles in an incident parallel beam are deviated by a specified amount. We imagine a 

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