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(B) For a hydrogen atom,$Z = 1$. The Rydberg formula is $\frac{1}{\lambda} = R_H 	imes (1)^2 	imes \left( \frac{1}{n_1^2} - \frac{1}{n_2^2} ight)$

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$486$

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(B) For a hydrogen atom,$Z = 1$. The Rydberg formula is $\frac{1}{\lambda} = R_H 	imes (1)^2 	imes \left( \frac{1}{n_1^2} - \frac{1}{n_2^2} ight)$.Given $n_1 = 2$ and $n_2 = 4$,and $R_H = 1.097 	imes 10^7 \ m^{-1}$.$\frac{1}{\lambda} = 1.097 	imes 10^7 	imes \left( \frac{1}{2^2} - \frac{1}{4^2} ight) = 1.097 	imes 10^7 	imes \left( \frac{1}{4} - \frac{1}{16} ight)$.$\frac{1}{\lambda} = 1.097 	imes 10^7 	imes \left( \frac{3}{16} ight) = 2.0568 	imes 10^6 \ m^{-1}$.$\lambda = \frac{1}{2.0568 	imes 10^6} \approx 4.86 	imes 10^{-7} \ m = 486 \ nm$.

List-$I$ (Spectral Series for Hydrogen)	List-$II$ (Spectral Region)
$A$. Lyman	$I$. Infrared region
$B$. Balmer	$II$. $UV$ region
$C$. Paschen	$III$. Infrared region
$D$. Pfund	$IV$. Visible region

The wavelength of radiation emitted when an electron falls from the $4^{th}$ Bohr orbit to the $2^{nd}$ in an $H$ atom is .............. $nm$.

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Match List-$I$ with List-$II$.

List-$I$ (Spectral Series for Hydrogen) List-$II$ (Spectral Region)

$A$. Lyman $I$. Infrared region

$B$. Balmer $II$. $UV$ region

$C$. Paschen $III$. Infrared region

$D$. Pfund $IV$. Visible region

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