Question

In hydrogen spectrum, the ratio of wavelengths of the last line of Lyman series and that of the last line of Balmer series is ______.

Options

• 1

• 0.5

• 0.25

• 0.2

Answer 1

In hydrogen spectrum, the ratio of wavelengths of the last line of Lyman series and that of the last line of Balmer series is 0.25.

Explanation:

Wavelength, \[\frac {1}{λ}\] = R \[\left(\frac{1}{\mathrm{n}^2}-\frac{1}{\mathrm{m}^2}\right)\]

For last line of Lyman series: n = 1, m = ∞

\[\frac{1}{\lambda_{_L}}=\mathbf{R}\left(\frac{1}{1^2}\quad\frac{1}{\infty^2}\right)=\mathbf{R}\]   ...(i)

For last line of Balmer series: n = 2, m = ∞

\[\frac{1}{\lambda_{_B}}=\mathbf{R}\left(\frac{1}{2^{2}}-\frac{1}{\infty^{2}}\right)=\frac{\mathbf{R}}{4}\]   ...(ii)

Dividing equation (ii) by equation (i),

\[\frac{\lambda_\mathrm{L}}{\lambda_\mathrm{B}}=\frac{\mathrm{R}/4}{\mathrm{R}}=\frac{1}{4}=0.25\]