Question

Calculate the energy to be imparted to an α-particle to force it into the nucleus of ²³⁸₉₂U (r₀ = 1.2fm)

Answer 1

The energy required to force an α-particle(classically) into a nucleus of charge Ze is equal to the potential energy at the barrier height and is given by 

E = zZe²/4πε₀R. 

This is barely possible when α particle and the Uranium nucleus will just touch each other and the kinetic energy of the bombarding particle is entirely converted into potential energy. 

R = R₁ + R₂ = r(A^1/3₁ + A₂^1/3) 

= 1.2(4^1/3 + 238^1/3) = 9.34fm 

E = 1.44zZ/R = 1.44 × 2 × 92/9.34 = 28.37MeV