Question

The ratio of areas within the electron orbits for the first excited state to the ground state for hydrogen atom is

• A. 16 : 1
• B. 18 : 1
• C. 4 : 1
• D. 2 : 1

Answer 1

Answer: (A)

16 : 1

Answer 2

For a hydrogen atom

Radius $r \propto n^{2}$ ⇒ $\frac{r_{1}^{2}}{r_{2}^{2}} = \frac{n_{1}^{4}}{n_{2}^{4}}$ ⇒ $\frac{\pi r_{1}^{2}}{\pi r_{2}^{2}} = \frac{n_{1}^{4}}{n_{2}^{4}}$

⇒ $\frac{A_{1}}{A_{2}} = \frac{n_{1}^{4}}{n_{2}^{4}} = \frac{2^{4}}{1^{4}} = 16$ ⇒ $\frac{A_{1}}{A_{2}} = \frac{16}{1}$