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  4. 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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Q. 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

Structure of Atom

Solution:

According to Rydberg equation
$\frac{1}{\lambda}=R \left(\frac{1}{x^{2}}-\frac{1}{y^{2}}\right)$
$R =109678 \,cm^{-1} ; x=2 y=4$
$ \frac{1}{\lambda}=109678 \left[\frac{1}{4}-\frac{1}{16}\right] =109678 \times\frac{3}{16}$
On solving, $\lambda=486 \,mn$