First slide

Hydrogen spectrum

Question

If $λ_{1}$ and $λ_{2}$ are the wavelengths of the first members of the Lyman and Paschen series, respectively, then $λ_{1} : λ_{2}$ is

Moderate

A

1:3
B

1:30
C

7:50
D

7:108

Solution

$For Lyman series, n_{1} = 1 and n_{2} = 2 for first line$
$\frac{1}{λ_{1}} = R [\frac{1}{1^{2}} - \frac{1}{2^{2}}] = R [\frac{1}{1} - \frac{1}{4}] = \frac{3 R}{4}$
$For Paschen series, n_{1} = 3 and n_{2} = 4 for first line$
$\begin{array}{rcl} ∴ \frac{1}{λ_{2}} & = & R [\frac{1}{3^{2}} - \frac{1}{4^{2}}] = R [\frac{1}{9} - \frac{1}{16}] = \frac{7 R}{144} \\ \frac{λ_{1}}{λ_{2}} & = & \frac{4 / 3 R}{144 / 7 R} = \frac{7}{108} \end{array}$

Get Instant Solutions

When in doubt download our app. Now available Google Play Store- Doubts App

Recieve an sms with download link

Doubts App

OR

SCAN ME

Doubts App

Doubts App