The ratio of the areas of the electron orbits for the second excited state to the first excited state for…

The ratio of the areas of the electron orbits for the second excited state to the first excited state for the hydrogen atom is
  1. $3: 2$
  2. $9: 4$
  3. 16:81
  4. 81:16

Solution

$\begin{aligned} & r_n \propto n^2 \Rightarrow A_n \propto n^4 \text { where, } A_n=\text { area } \\ \therefore \quad & \frac{A_3}{A_2}=\left(\frac{3}{2}\right)^4=\frac{81}{16}\end{aligned}$

Asked in: MHT CET 2024 (15 May Shift 1)

Practice more Structure of Atoms and Nuclei questions on Aicharya