Question

In hydrogen spectrum, the shortest wavelength in the Balmer series is λ. The shortest wavelength in the Bracket series is _____.

Options

• 4 λ

• 9 λ

• 16 λ

• 2 λ

Answer 1

In hydrogen spectrum, the shortest wavelength in the Balmer series is λ. The shortest wavelength in the Bracket series is 4 λ.

Explanation:

\[\frac{1}{\lambda}=RZ^{2}\left[\frac{1}{n_{f}^{2}}-\frac{1}{n_{i}^{2}}\right]\]

For minimum wavelength, energy is maximum, So, 

n_i = ∞

For Balmer series, n_f  = 2, and for Brackett series, n_f  = 4.

\[\frac{1}{\lambda}=\frac{R}{4}\]

\[\frac{1}{\lambda_\mathrm{brackett}}=\frac{R}{16}\]

\[\frac{\lambda_{\mathrm{brackett}}}{\lambda}=\frac{R}{4}\times\frac{16}{R}\]

λ_brackett = 4λ