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Q)

Calculate the wavelength emitted during the transition of electron in between two levels of $Li^{+2}$ ion whose sum is 4 and difference is 2.

$\begin{array}{1 1}(a)\;1.14\times 10^{-2}cm&(b)\;2.3\times 10^{-6}cm\\(c)\;1.14\times 10^{-6}cm&(d)\;2.4\times 10^{-3}cm\end{array}$

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A)
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Let the transition occurs in between the levels $n_1$ and $n_2$.Thus if $n_2 > n_1$,then
$n_1+n_2=4$
$n_2-n_1=2$
$n_1=1$ and $n_2=3$
$\therefore \large\frac{1}{\lambda}$$=R_H\times z^2\big[\large\frac{1}{1^2}-\frac{1}{3^2}\big]$
$z=3$ for Li
$\Rightarrow 109678\times 3^2\times \large\frac{8}{9}$
$\lambda=1.14\times 10^{-6}cm$
Hence (c) is the correct answer.
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