Question

With increase in principal quantum number n, the energy difference between adjacent energy levels in hydrogen atom

• A. increases
• B. decreases
• C. remains constant
• D. decreases for lower values of n and increases for higher values of n

Answer 1

Answer: (B)

The energy differences between adjacent energy levels in an atom is given by the following relation $\Delta E=\frac{R_H{Z}^2}{hc}\left[\frac{1}{n_1^2}-\frac{1}{n_2^2}\right]$ or $\Delta E\propto \left[\frac{1}{n_1^2}-\frac{1}{n_2^2}\right]$ ie, energy difference between adjacent energy levels is inversely proportional to the principal quantum number, n. Therefore, with increase in n, the energy difference will decrease.