Question

The wavelength of radiation emitted due to transition of electron from energy level E to zero is equal to $\lambda$ . The wavelength of radiation ${\lambda }_1$ emitted when electron jumps from energy level $\frac{3E}{2}$ to zero will be.

• A. $\frac{2}{3}\lambda$
• B. $\frac{3}{2}\lambda$
• C. $\frac{4}{9}\lambda$
• D. $\frac{9}{4}\lambda$

Answer 1

Answer: (A)

$\frac{2}{3}\lambda$

$\text{Energy}=\frac{hc}{\lambda }$

$\begin{array}{c}\text{For}{1}^{\text{st}}\text{case}\\ (E-0)=\frac{hc}{\lambda }-\left(i\right)\end{array}$

$\begin{array}{c}\text{for 2nd case}\\ (\frac{3E}{2}-0)=\frac{hc}{{\lambda }_1}-\left(ii\right)\end{array}$

$\begin{array}{c}\text{equation (i)}÷\text{(ii)}\\ \begin{array}{c}\frac{{\lambda }_1}{\lambda }=\frac{2}{3}\\ {\lambda }_1=\frac{2}{3}\lambda \end{array}\end{array}$