Question

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

• A. $\frac{8}{9}{R}_H$
• B. $\frac{32}{9}{R}_H$
• C. $\frac{1}{9}{R}_H$
• D. none of these

Answer 1

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

Let take states be $n_1$ and $n_2$

$\therefore n_1+n_2=4$

$n_1-n_2=2$

$\therefore n_1=3\to n_2=1$

$\overline{\nu }=R_H\times z^2(\frac{1}{n_2^1}-\frac{1}{n_2^2})$

$=R_H\times 4(1-\frac{1}{9})$ $(z$ for $H{e}^{+}=2)$

$=R_H\times 4\times \frac{8}{9}$

$=\frac{32}{9}{R}_H$