Question

Wave number of spectral line for a given transition is $x cm ^{-1}$ for $He ^{+}$, then its value for $Be ^{3+}$ (isoelectronic of $He ^{+}$ ) for same transition is

• A. $ \frac{x}{4}c{{m}^{-1}} $
• B. $ x\,c{{m}^{-1}} $
• C. $ 4x\,c{{m}^{-1}} $
• D. $ 16x\,c{{m}^{-1}} $

Answer 1

Answer: (C)

$\bar{v}$ (wave number) $=\bar{R}_{H} Z^{2}\left[\frac{1}{n_{1}^{2}}-\frac{1}{n_{2}^{2}}\right]$
$\bar{v}_{1}\left(H e^{+}, Z=2\right)=\bar{R}_{H}(2)^{2}\left[\frac{1}{n_{1}^{2}}-\frac{1}{n_{2}^{2}}\right]$
$\bar{v}_{2}\left(B e^{3+}, Z=4\right)=\bar{R}_{H}=(4)^{2}\left[\frac{1}{n_{1}^{2}}-\frac{1}{n_{2}^{2}}\right]$
$\therefore \frac{v_{2}}{v_{1}}=\frac{(4)^{2}}{(2)^{2}}$
$=\frac{16}{4}=4 $
$\therefore \bar{v}_{2}=4 \bar{v}_{1}$
$ \bar{v}_{2}=4 \times c m^{-1}$