Question

The ratio of the wavelengths of the longest wavelength lines in the Lyman and Balmer series of hydrogen spectrum is

• A. $\frac{3}{23}$
• B. $\frac{5}{27}$
• C. $\frac{7}{29}$
• D. $\frac{9}{39}$

Answer 1

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

The longest wavelengths in the two series are given by
$\frac{1}{{\lambda }_L}=R(\frac{1}{1^2}-\frac{1}{2^2})=\frac{3}{4}R$
and $\frac{1}{{\lambda }_B}=R(\frac{1}{2^2}-\frac{1}{3^2})=\frac{5}{36}R$
$\therefore \frac{{\lambda }_L}{{\lambda }_B}=\frac{4}{3}\times \frac{5}{36}=\frac{5}{27}$
Hence, the correct choice is (b).