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The wavelength of the spectral line when the electron in the hydrogen atom undergoes a transition from the energy level 4 to energy level 2 is

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$486 nm$

$486 m$

$486 A^{o}$

$486 cm$

answer is A.

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Detailed Solution

According to Rydberg equation

$\begin{array}{l} \frac{1}{λ} = R (\frac{1}{n_{1}^{2}} - \frac{1}{n_{2}^{2}}) \\ R = 109678 {cm}^{- 1}; n_{1} = 2; n_{2} = 4 \\ \frac{1}{λ} = 109678 [\frac{1}{4} - \frac{1}{16}] = 109678 \times \frac{3}{16} \\ On solving, λ = 486 nm \end{array}$

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