Question

The atomic spectrum of ${Li}^{+2}$ arises due to the transition of an electron from $n_2$ to $n_1.$ If $(n_1+n_2)=4$ and $(n_2-n_1)=2$ find the wavelength of the $3^{rd}$ line of this series in $L{i}^{+2}$ ion ?

• A. $10.8nm$
• B. $1.08nm$
• C. $108nm$
• D. $100nm$

Answer 1

The correct option is A $10.8nm$

$\begin{array}{c}\text{Given,}{n}_1+n_2=4\\ n_2-n_2=2\\ \text{By solving two equations}{n}_1=1,n_2=3\\ 3^{rd}\text{line of series is from}2\text{to}1\end{array}$

$\begin{array}{c}\frac{1}{\lambda }=R(3{)}^2[1-\frac{1}{4}]\\ \sqrt{\lambda }=10.8nm\end{array}$