$(a)\;4500A^{\large\circ}\qquad(b)\;5600A^{\large\circ}\qquad(c)\;2600A^{\large\circ}\qquad(d)\;6500A^{\large\circ}$

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First Line is called $\alpha$ line

Second line is called as $\beta$ line

$\large\frac{1}{\lambda} = \overline R_HZ^2[\large\frac{1}{n_1^2}-\large\frac{1}{n_2^2}]$

For Balmer Series $n_1$=2 and for $\beta$ line $n_2$=4

$\large\frac{1}{\lambda_\beta} = \overline R_HZ^2[\large\frac{1}{2^2}-\large\frac{1}{4^2}]$

$=\large\frac{3}{16} \overline R_HZ^2$

For $\alpha$-line $n_2$ = 3 For same series

$\large\frac{1}{\lambda_\beta} = \overline R_HZ^2[\large\frac{1}{2^2}-\large\frac{1}{3^2}]$

$=\large\frac{5}{16} \overline R_HZ^2$

$\large\frac{\lambda_{\beta'}}{\lambda_\beta}=\large\frac{3}{16}\times \large\frac{36}{5}$

$\lambda_{\beta'} = 4815\times10^{-10}\times \large\frac{108}{80}$

$=6.5\times10^{-7}$

$=6500A^{\large\circ}$

Hence answer is (d)

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