Question

Determine the wavelength emitted for an electronic transition from M shell $(n=3)$ to K shell $(n=1)$ in a hydrogen atom.$(R=109,677c{m}^{-1})$

• A. $1026A^{\circ }$
• B. $10.26A^{\circ }$
• C. $513A^{\circ }$
• D. $2032A^{\circ }$

Answer 1

The correct option is A $1026A^{\circ }$

Applying the formula $\frac{1}{\lambda }=R_H[\frac{1}{n_1^2}-\frac{1}{n_2^2}]$ where $n_1=1$ and $n_2=3$

$\frac{1}{\lambda }=R_H[\frac{1}{1^2}-\frac{1}{3^2}]$ = $R_H[\frac{1}{1}-\frac{1}{9}]$ = $\frac{1}{\lambda }=109677\times \frac{8}{9}=97491c{m}^{-1}$

$\lambda =\frac{1}{97491}=1.026\times {10}^{-5}cm=1026A^{\circ }$