Question

The ratio of the longest to shortest wavelengths in Brackett series of hydrogen spectrum is

• A. $\frac{25}{9}$
• B. $\frac{17}{6}$
• C. $\frac{9}{5}$
• D. $\frac{4}{3}$

Answer 1

Answer: (A)

$$\begin{gathered} \frac{1}{{\lambda }_{\max }}=R\left[\frac{1}{4^2}-\frac{1}{5^2}\right]=\frac{9}{25\times 16}R \\ \text{ and }\frac{1}{{\lambda }_{\min }}=R\left[\frac{1}{4^2}-\frac{1}{{\infty }^2}\right]=\frac{R}{16} \\ \therefore \frac{{\lambda }_{\max }}{{\lambda }_{\min }}=\frac{25}{9} \end{gathered}$$