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# A series of lines in the spectrum of atomic H lies at wavelengths 656.46 , 486.27 , 434.17 , 410.29 mm. what is the wavelength of next line in this series?

$(a)\;493.3 nm\qquad(b)\;397.2nm\qquad(c)\;593.4nm.\qquad(d)\;392.3nm$

The given series lies in the visible region and thus appears to be Balmer series
Given:
$n_1$ = 2
$\lambda = 410.29 \times10^{-7}$ cm
$n_2 = ?$
$\large\frac{1}{\lambda}$= $R_H[\large\frac{1}{n_1^2}-\large\frac{1}{n_2^2}]$
$\large\frac{1} {410.29\times10^{-7}}$= $109678[\large\frac{1}{n_1^2}-\large\frac{1}{n_2^2}]$
$n_2$ = 6
Next line will be obtained during the jump of electron from $7^{th}$ to $2^{nd}$ shell
$\large\frac{1}{\lambda}$= $R_H[\large\frac{1}{2^2}-\large\frac{1}{7^2}]$
= $109678[\large\frac{1}{4}-\large\frac{1}{49}]$
$\lambda = 397.2\times10^{-7}$ cm
$\lambda = 397.2$ nm