Can the transition $\mathbf{2}\mathbf{s}\to \mathbf{1}\mathbf{s}$ in the hydrogen atom occur by electric dipole radiation? The lifetime of the 2 s is known to be unusual. Is it unusually short or long?

The oscillating electric dipole is possibly the vital source for the electromagnetic radiations. The electric dipole is placed in a particular electric field and given with some disturbance to produce oscillations, that is responsible for producing the electromagnetic radiations.

From the selection rules of the electric dipole radiation, the change of / in the transition must be 1 or -1. Thus, the $2\mathrm{s}\to 1\mathrm{s}$transition can't occur by the electric dipole radiation, since the change in / would be zero.

Since that the most efficient radiation is given by an oscillating electric dipole and it is known that the $2\mathrm{s}\to 1\mathrm{s}$transition can't occur by electric dipole radiation. It is expected that the electron will spend relatively long time in the 2 s before transitioning to the 1s via other inefficient (unlike) types of radiation. Thus, it is anticipated that the lifetime of the 2s state be unusually long.

Therefore, transition can’t occur by the electric dipole radiation. The electron will spend relatively long time in the 2s before transitioning to the 1s. Thus, we anticipate that the lifetime of the 2s state be unusually long.