Question

An electronic transition from $M$ shell (n = 3) to $K$ shell (n =1) takes place in a hydrogenatom. Find the wavelength of radiation emited. ($R=$ 109, 677 $c{m}^{-1}$).

• A. $1026A^o$
• B. $1.026\times {10}^{-5}m$
• C. $1.026\times {10}^{-3}cm$
• D. none of these

Answer 1

Answer: (A)

$1026A^o$

For a hydrogen atom,

$\frac{1}{\lambda }=R[\frac{1}{{n_1}^2}-\frac{1}{{n_2}^2}]$

Given $n_1=1$ , $n_2=3$

$\frac{1}{\lambda }=R[1-\frac{1}{9}]$

$\frac{1}{\lambda }=\frac{1}{R}\left[\frac{9}{8}\right]$

$=1.0257$ x ${10}^{-5}$ cm

$=1025.7$ x ${10}^{-10}$ m

$\approx$ $1026$ $\mathring{A}$