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  4. The wave number of the first line of Balmer series of hydrogen is 15200 cm -1. The wave number of the first Balmer line of Li 2+ ion is

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Q. The wave number of the first line of Balmer series of hydrogen is $15200 \,cm ^{-1}$. The wave number of the first Balmer line of $Li ^{2+}$ ion is

Structure of Atom

Solution:

$\bar{v}_{ H _2}^{\oplus}=R\left(\frac{1}{n_1^2}-\frac{1}{n_2^2}\right)=15200\, cm ^{-1}$
$\bar{v}_{ Li ^{2+}}=R Z^2\left(\frac{1}{n_1^2}-\frac{1}{n_2^2}\right)=3^2 \times 15200$
$=136800\, cm ^{-1}$