First slide

Bohr Model of the Hydrogen atom.

Question

The limit of Balmer series is 8646 $Å$ The wavelength of the first member of this series will be

Moderate

A

$6563 Å$
B

$3646 Å$
C

$7200 Å$
D

$1000 Å$

Solution

$\frac{1}{λ} = R [\frac{1}{{n_{1}}^{2}} - \frac{1}{{n_{2}}^{2}}] For the limit of Balmer series, we have \frac{1}{λ_{lim}} = R [\frac{1}{2^{2}} - \frac{1}{\infty}] = \frac{R}{4} and \frac{1}{λ_{first}} = R [\frac{1}{2^{2}} - \frac{1}{3^{2}}] = \frac{5 R}{36} λ_{first} = λ_{lim} (\frac{36}{5 \times 4}) = 3646 \times \frac{9}{5} = 6563 Å$

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