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

The potential energy of a proton and an electron in a hydrogen atom is given by $V = V_0 \ln(r/r_0)$,where $r_0$ is a constant. Assuming the Bohr model is applicable to this system,find the relationship between the radius $r_n$ and the principal quantum number $n$.

Using Bohr's atomic model,derive an equation for the radius of the $n^{th}$ orbit of an electron.

The ratio of kinetic energy to the total energy of an electron in a Bohr orbit of the hydrogen atom is

In a hydrogen atom,the electron is moving around the nucleus with a velocity of $2.18 \times 10^{6} \; m/s$ in an orbit of radius $0.528 \; \mathring{A}$. The acceleration of the electron is:

When the electron orbiting in a hydrogen atom goes from one orbit to another orbit (principal quantum number $= n$),the de-Broglie wavelength $(\lambda)$ associated with it is related to $n$ as: