The $21\, cm$ radio wave emitted by hydrogen in interstellar space is due to the interaction called the hyperfine interaction in atomic hydrogen. The energy of the emitted wave is nearly

When a hydrogen atom is in its first excited level,its radius is .... of the Bohr radius.

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

Consider a hydrogen atom with its electron in the $n^{\text{th}}$ orbital. An electromagnetic radiation of wavelength $90 \ nm$ is used to ionize the atom. If the kinetic energy of the ejected electron is $10.4 \ eV$,then the value of $n$ is $(hc = 1242 \ eV \ nm)$.

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

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