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.