The magnetic field at the centre due to the motion of an electron in the first Bohr orbit is $B$. The magnetic field due to the motion of an electron in the second Bohr orbit at the centre will be

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 $(i) R = 0.1 \mathring{A}$ and $(ii) R = 10 \mathring{A}$.

In a hydrogen atom,the radius of the $n^{th}$ Bohr orbit is $r_n$. The graph between $\log \left( \frac{r_n}{r_1} \right)$ and $\log n$ will be:

Would the Bohr formula for the $H-$ atom remain unchanged if the proton had a charge of $+ \frac{4e}{3}$ and the electron a charge of $- \frac{3e}{4}$ (where $e = 1.6 \times 10^{-19} \ C$)? Give reasons for your answer.

In which of the following systems will the radius of the first orbit $(n = 1)$ be minimum?

In a hydrogen atom,the electron and proton are bound at a distance of about $0.53 \; \mathring{A}$.
$(a)$ Estimate the potential energy of the system in $eV$,taking the zero of the potential energy at infinite separation of the electron from the proton.
$(b)$ What is the minimum work required to free the electron,given that its kinetic energy in the orbit is half the magnitude of potential energy obtained in $(a)$?
$(c)$ What are the answers to $(a)$ and $(b)$ above if the zero of potential energy is taken at $1.06 \; \mathring{A}$ separation?