Question

Wave number of spectral line for a given transition is $xc{m}^{-1}$ for $H{e}^{+}$, then its value for $B{e}^{3+}$ (isoelectronic of $H{e}^{+}$ ) for same transition is

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

Answer 1

Answer: (C)

$\bar{v}$ (wave number) $={\bar{R}}_H{Z}^2\left[\frac{1}{n_1^2}-\frac{1}{n_2^2}\right]$
${\bar{v}}_1\left(H{e}^{+},Z=2\right)={\bar{R}}_H(2{)}^2\left[\frac{1}{n_1^2}-\frac{1}{n_2^2}\right]$
${\bar{v}}_2\left(B{e}^{3+},Z=4\right)={\bar{R}}_H=(4{)}^2\left[\frac{1}{n_1^2}-\frac{1}{n_2^2}\right]$
$\therefore \frac{v_2}{v_1}=\frac{(4{)}^2}{(2{)}^2}$
$=\frac{16}{4}=4$
$\therefore {\bar{v}}_2=4{\bar{v}}_1$
${\bar{v}}_2=4\times c{m}^{-1}$