Among the following electronic transitions in a hydrogen atom, which one corresponds to the emission

Question

Among the following electronic transitions in a hydrogen atom, which one corresponds to the emission of a photon with the maximum wavelength?

Professor PC Thomas Classes · Answer

(d) : The energy of an emitted photon is $\Delta E = hc/\lambda$. Maximum wavelength corresponds to the minimum energy difference between the specified levels. The energy gap between adjacent energy levels in a hydrogen atom decreases drastically as the principal quantum number $n$ increases ($\Delta E \propto \frac{1}{n_1^2} - \frac{1}{n_2^2}$). The transition $n=5 	o n=4$ involves the highest energy levels among the choices, and thus has the smallest energy gap, leading to the maximum wavelength.