Question

Ratio of longest wave lengths corresponding to Lyman and Balmer series in hydrogen spectrum is -

• A. $\frac{5}{27}$
• B. $\frac{3}{23}$
• C. $\frac{7}{29}$
• D. $\frac{9}{31}$

Answer 1

The correct option is A $\frac{5}{27}$

$\frac{1}{{\lambda }_l}=R(1{)}^2[\frac{1}{1^2}-\frac{1}{2^2}]=\frac{3R}{4}$
${\lambda }_l=\frac{4}{3R}$ $\cdots \left(1\right)$
$\frac{1}{{\lambda }_b}=R(1{)}^2[\frac{1}{2^2}-\frac{1}{3^2}]=\frac{5R}{36}$
${\lambda }_b=\frac{36}{5R}$ $\cdots \left(2\right)$
$\frac{{\lambda }_l}{{\lambda }_b}=\frac{4}{3R}\times \frac{5R}{36}=\frac{5}{3\times 9}=\frac{5}{27}$