Atoms and Nuclei: JEE Main 2018 Physics question

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 ${\Lambda _n}$ 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)