When we developed Gamow's theory of alpha emission, we assumed the alpha particle was preformed in the nucleus. there is some evidence that nucleon clusters continually form and breakup in the nucleus and that alpha emission requires the formation of an alpha cluster at the nuclear surface prior to emission. Using classical (i.e. not quantum mechanics) arguments, come up with an estimate for the probability of an alpha particle being formed at the surface of a nucleus. Calculate your probability for a nucleus with A=238
First, in the classical fashion we take a nucleus to be a sphere filled with A nucleons, each of volume V1 so that the whole sphere has volume
V = A*V1
In this model the 238 nucleus has radius
R = ...
The solution uses classical arguments to come up with an estimate for the probability of an alpha particle being formed.