Question

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

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

Answer 1

The correct option is A $\frac{25}{9}$

For Bracket series: $\frac{1}{{\lambda }_{max}}=R[\frac{1}{4^2}-\frac{1}{5^2}]=\frac{9}{25\times 16}R$
$\frac{1}{{\lambda }_{min}}=R[\frac{1}{4^2}-\frac{1}{{\infty }^2}]=\frac{R}{16}\Rightarrow \frac{{\lambda }_{max}}{{\lambda }_{min}}=\frac{25}{9}$