Rutherford scattering by computer

You will write three functions for the scattering of alpha particles by a nucleus.

The idea. In a head-on hit the closest approach is $r_0 = \dfrac{2Z \times 1.44}{K}$ in fm, with $K$ in MeV. The angle of deflection follows $\tan\dfrac{\theta}{2} = \dfrac{r_0}{2b}$.

Your tasks.

1. In closest_approach, return $r_0$ in fm for a nucleus with charge $Z$ and an alpha particle of energy $K$ in MeV.
2. In deflection, return the angle of deflection, in degrees, for the impact parameter $b$.
3. In impact_parameter, return the impact parameter, in fm, that gives a chosen angle of deflection.