Question

What will be the ratio of the wavelength of the first spectral line to that of the second line of the Paschen series of hydrogen spectrum?

• A. 25:16
• B. 256:175
• C. 36:49
• D. 175:256

Answer 1

The correct option is B 256:175

First spectral line means $n_1=3$ and $n_2=4$.The second spectral line will have $n_1=3$ and $n_2=5$
We know,
$\frac{1}{\lambda }=R(\frac{1}{{n_1}^2}-\frac{1}{{n_2}^2})$
For first spectral line,
So, $\frac{1}{{\lambda }_1}=R(\frac{1}{3^2}-\frac{1}{4^2})$...(i) where ${\lambda }_1$ is the wavelength for first spectral line.
For second line, $\frac{1}{{\lambda }_2}=R(\frac{1}{3^2}-\frac{1}{5^2})$...(ii) where ${\lambda }_2$ is the wavelength for second spectral line.
Dividing equation (ii) by eq. (i),
$\frac{{\lambda }_1}{{\lambda }_2}$ = $\frac{16\times 16}{25\times 7}$
So ratio becomes 256:175.