Neco 2024 Physics Question 26

An isolated hydrogen atom is initially in the \( n = 5 \) energy level. In a weak uniform magnetic field the \( n = 3 \) level splits into three equally spaced sub‑levels with an energy separation of \( 1.0\times10^{-3}\) eV between adjacent sub‑levels. The atom decays by the two‑step path: first from \( n = 5 \) to the upper sub‑level of \( n = 3 \) (the sub‑level of highest energy), and then from that sub‑level to the ground state (\( n = 1 \)).\n\n(a) Calculate the wavelength (in nanometres, to three significant figures) of the photon emitted in the \( 5 \rightarrow 3 \) transition.\n\n(b) Calculate the wavelength (in nanometres, to three significant figures) of the photon emitted in the subsequent \( 3 \rightarrow 1 \) transition.\n\n(c) Find the difference between the two wavelengths (\( \Delta\lambda \)) in nanometres, to three significant figures.