First slide

Bohr Model of the Hydrogen atom.

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

$\frac{1}{λ} \propto (\frac{1}{{n_{1}}^{2}} - \frac{1}{{n_{2}}^{2}}); ∴ \frac{λ_{1}}{λ_{2}} = \frac{{(\frac{1}{3^{2}} - \frac{1}{4^{2}})}_{paschen}}{{(\frac{1}{1^{2}} - \frac{1}{2^{2}})}_{Lymen}} = \frac{7 / 144}{3 / 4} = \frac{7}{108}$

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