Question

The wave number of electromagnetic radiation emitted during the transition of electron in between the two levels of Li${}^{2+}$ ion whose principal quantum numbers sum is 4 and difference is 2, is:

• A. $3.5R$
• B. $4R$
• C. $8R$
• D. $8/9R$

Answer 1

The correct option is C $8R$

v = $R{Z}^2\left(\frac{1}{n_1^2}-\frac{1}{n_2^2}\right)$
Here,
$n_1+n_2=4$
$n_2-n_1=2$

By solving we get,
$n_1=1,n_2=3$

So, $\nu =R{Z}^2\left(\frac{1}{n_1^2}-\frac{1}{n_2^2}\right)$

= $R\times 3^2(\frac{1}{1^2}-\frac{1}{3^2})=8R$

Hence, option $C$ is correct.