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1900's Physics and Wave

What is the c...

Question

What is the colour corresponding to the wavelength of light emitted when the electron in a hydrogen atom undergoes transition from n= $4$ to n = $2$ ?

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Solution

Wavelength $= ?$
$\frac{1}{λ} = R_{H} (\frac{1}{n_{1}^{2}} - \frac{1}{n_{2}^{2}})$
$\frac{1}{λ} = R_{H} (\frac{1}{2^{2}} - \frac{1}{4^{2}})$
$= R_{H} (\frac{1}{4} - \frac{1}{16})$
$\frac{1}{λ} = R_{H} \times \frac{12}{16}$
$\frac{1}{λ} = \frac{3 R_{H}}{4}$
$λ = \frac{4}{3 R_{H}} = \frac{4}{3 \times 109677}$ cm $= 1.212 \times 10^{- 5}$
$= 121.2$ nm.

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