Energy of the Electron & Energy Levels question from NEET 2024

Answer: (d)

1. $\lambda = \frac{hc}{\Delta E}$, so $\lambda \propto \frac{1}{\Delta E}$.
2. $\lambda_1$: $-\frac{5E}{2} \to -4E$, $\Delta E = 1.5E$. $\lambda_2$: $-2E \to -3E$, $\Delta E = E$. $\lambda_3$: $-2E \to -4E$, $\Delta E = 2E$.
3. So $\lambda_2 > \lambda_1 > \lambda_3$ and $\frac{\lambda_2}{\lambda_3} = \frac{2E}{E} = 2$.
4. So the answer is (d) $\lambda_2 > \lambda_1,\ \lambda_2 = 2\lambda_3$.