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

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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

Hence answer is (b)

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