Question

An electric in hypothetical hydrogen atom is its 3rd excited state and makes. transition from 3rd and 2nd excited, then to 1st excited state and then to ground state. If the amount of time spend by the electron in any sate of quantum number n, is proportional to $\left(\frac{1}{n-1}\right)$, then the ratio of no. of revolution completed by the electric in 1st excited state to that in the 2nd excited state will be

• A. 2
• B. $\frac{27}{8}$
• C. $\frac{27}{4}$
• D. $\frac{27}{6}$

Answer 1

The correct option is A 2

$\begin{array}{c}\text{Given time stay}\propto \frac{1}{n-1}\\ \text{1st excided state}n=2\\ 2^{nd}\text{excited state}n=3\\ \text{Required ratio is}\\ \begin{array}{c}\frac{1}{2-1}:\frac{1}{3-1}\\ 1:\frac{1}{2}\end{array}\\ \therefore \text{Required ratio is}2:1.\end{array}$