AIIMS 2018 Physics Bohr Model MCQ Question

When an electron transitions from a higher energy level (radius $r_2$) to a lower energy level (radius $r_1$) in a hydrogen-like atom, the energy difference between these levels is given by the formula $E = \frac{K e^2}{r_1} - \frac{K e^2}{r_2}$. The wavelength of the emitted photon can be calculated using the relation $\lambda = \frac{hc}{E}$. Substituting the energy difference into this equation leads to the expression $\lambda = \frac{2ch r_1 r_2}{K e^2 (r_2 - r_1)}$, which matches option C.

Options A, B, and D do not correctly account for the factors of energy and the relationship between the radii, leading to incorrect coefficients or terms in their expressions.