Question

The wave number of the limiting line in Lyman series of hydrogen is 109678 $c{m}^{-1}$. The wave number of the limiting line in Balmer series of $H{e}^{+}$ would be :

• A. 54839 $c{m}^{-1}$
• B. 109678 $c{m}^{-1}$
• C. 219356 $c{m}^{-1}$
• D. 438712 $c{m}^{-1}$

Answer 1

Answer: (B)

Series limit of Lyman series, $n_1=1;n_2=\infty$
$\therefore$ wave number is given by -
$\bar{\gamma }=R\left[\frac{1}{n_1^2}-\frac{1}{n_2^2}\right]$
$\left[\because R=109678c{m}^{-1}\right]$
$\Rightarrow \bar{\gamma }=109678\left[\frac{1}{12}-\frac{1}{{\infty }^2}\right]c{m}^{-1}$.
$\Rightarrow \bar{\gamma }=109678[1-0]c{m}^{-1}$.
$\Rightarrow \bar{\gamma }=109678c{m}^{-1}$ .