Question

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

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

Answer 1

Answer: (B)

109678 $cm^{-1}$

Answer 2

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