Question

Of the following transition in $H$-atom, the one which gives an absorption line of maximum wavelength is:

• A. $n=1\to n=2$
• B. $n=3\to n=8$
• C. $n=2\to n=1$
• D. $n=3\to n=1$

Answer 1

The correct option is B $n=3\to n=8$

Absorption spectrum is observed when an electronic transition takes place from a lower level to a higher energy level. So options (c) and (d) cannot be correct.

For the transition $n=1\to n=2$,
$\frac{1}{{\lambda }_1}=R_H[\frac{1}{1^2}-\frac{1}{2^2}]$

$\Rightarrow {\lambda }_1=\frac{4}{3R_H}=\frac{1.33}{R_H}...\left(i\right)$

For transition $n=3\to n=8$
$\frac{1}{{\lambda }_2}=R_H[\frac{1}{3^2}-\frac{1}{8^2}]$

$\Rightarrow {\lambda }_2=\frac{576}{55R_H}=\frac{10.47}{R_H}...\left(ii\right)$

Comparing equations (i) and (ii), we get that the transition $n=3\to n=8$ gives an absorption line of maximum wavelength.