Question

Find the value of wave number $\left(\nu ̅\right)$ in terms of Rydberg’s constant, when the transition of an electron takes place between the two levels of $H{e}^{+}$ ions whose sum is 4 and difference is 2.

• A. $\frac{8R}{9}$
• B. $\frac{32R}{9}$
• C. $\frac{3R}{4}$
• D. None of these

Answer 1

The correct option is B $\frac{32R}{9}$

Let $x>y$
$x+y=4i$
$x-y=2ii$
by solving $i$ and $ii$
$x=3andy=1$
$\stackrel{-}{v}=R(\frac{1}{n_f^2}-\frac{1}{n_i^2})Z^{2}c{m}^{-1}$
$\stackrel{-}{v}=R(\frac{1}{1^2}-\frac{1}{3^2})Z^{2}c{m}^{-1}$
$\stackrel{-}{v}=\frac{32R}{9}$