Which state of triply ionised beryllium $(Be^{3+})$ has the same orbital radius as that of the ground state of hydrogen?

In a hydrogen-like ion,the energy difference between the $2^{\text{nd}}$ excitation state and the ground state is $108.8 \ eV$. The atomic number of the ion is:

Given below are two statements $:$ one is labelled as Assertion $A$ and the other is labelled as Reason $R$.
Assertion $A :$ The Bohr model is applicable to hydrogen and hydrogen$-$like atoms only.
Reason $R :$ The formulation of Bohr model does not include repulsive force between electrons.
In the light of the above statements,choose the correct answer from the options given below $:$

If the atom $_{100}Fm^{257}$ follows the Bohr model and the radius of the outermost shell of $_{100}Fm^{257}$ is $n$ times the Bohr radius,then find $n$.

Find the radius of $Be^{3+}$ ions in its ground state assuming Bohr's model to be valid $(a_0 = 53 \ pm)$. (in $pm$)

The angular momentum of an electron in the $n^{th}$ orbit is given by: