A mass spectator known as a calutron is designed to separate fissionable uranium$-235$ atoms from non$-$fissionable uranium$-238$ atoms. The first calutron was built for the Manhattan Project in World War II$.$ The goal of the Manhattan project was the development of the atomic bomb.

a$)$ Calculate the ratio of the radius for a U$-238$ atom compared to that of a U$-235$ atom.

b$)$ The radius of the magnetic field in the calutron was approximately $1\mathrm{.}22$m$.$ How far apart were the slits for the two isotopes?