Question

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

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

Answer 1

Answer: (A)

For the Brackett series, $\frac{1}{{\lambda }_{max}}=R\left[\frac{1}{4^2}-\frac{1}{5^2}\right]=\frac{9}{25\times 16}R$
and
$\frac{1}{{\lambda }_{min}}=R\left[\frac{1}{4^2}-\frac{1}{{\infty }^2}\right]=\frac{R}{16}$
Therefore, $\frac{{\lambda }_{max}}{{\lambda }_{min}}=\frac{25}{9}$