If a proton had a radius R and the charge was uniformly distributed, calculate using Bohr theory, the ground state energy of a H-atom when (i) R=0.1 Å and (ii) R=10 Å.

Hint: The electrostatic force of attraction between positively charged nucleus and negatively charged electrons (Coulombian force) provides necessary centripetal force of revolution.
Step 1: Find the value of the Bohr radius.
$\frac{{\mathrm{mv}}^{2}}{{\mathrm{r}}_{\mathrm{B}}}=-\frac{{\mathrm{e}}^{2}}{{\mathrm{r}}_{\mathrm{B}}^{2}}·\frac{1}{4{\mathrm{\pi \epsilon }}_{0}}$
By Bohr's postulates in the ground state, we have;
$\mathrm{mvr}=\frac{\mathrm{h}}{2\mathrm{\pi }}$
On solving,
Step 2: Find the potential energy and kinetic energy.
The potential energy is given by;
Now, for a spherical nucleus of radius R.
Step 3: Find the value of the Bohr radius for R.
If R<rB, same result.
If R>>rB, the electron moves inside the sphere with radius r'B (r'B=new Bohr radius).