JEE Main 2018 — Atomic Physics Question with Solution

An electron from various excited states of hydrogen atom emit radiation to come to the ground state. Let ${\lambda }_n, {\lambda }_g$ be the de Broglie wavelength of the electron in the $n^{th}$ state and the ground state respectively. Let ${\wedge }_n$ be the wavelength of the emitted photon in the transition from the $n^{th}$ state to the ground state. For large n, (A, B are constants)