Question

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

• A. $\frac{8R}{9}$
• B. $\frac{32R}{9}$
• C. $\frac{3R}{4}$
• D. $\frac{9R}{4}$

Answer 1

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

Let, the $n_1$ and $n_2$ be the levels, where electronic transition is taking place.
According to the question,
$n_2+n_1=4n_2-n_1=2$
$\therefore n_1=1,n_2=3$
We know that,
$\overline{\nu }=R(Z{)}^2[\frac{1}{n_1^2}-\frac{1}{n_2^2}]$
Since, we are considering $H{e}^{+}$ ion,
$\therefore \overline{\nu }=R(2{)}^2[\frac{1}{1^2}-\frac{1}{3^2}]=\frac{32R}{9}$