Question

Calculate the wavelength emitted during the transition of electron in between two levels of $L{i}^{2+}$ ion whose sum is $4$ and difference is $2$.

• A. $\lambda =104\times {10}^{-6}cm$
• B. $\lambda =9.12\times {10}^{-6}cm$
• C. $\lambda =1.14\times {10}^{-6}cm$
• D. $\lambda =1.27\times {10}^{-7}cm$

Answer 1

Answer: (C)

$\lambda =1.14\times {10}^{-6}cm$

Let the transition occurs in between the levels $n_1$ and $n_2$. Thus, if then given
$n_1+n_2=4$
$n_2-n_1=2$ $\therefore n_2=3,n_1=1$
Therefore, $\frac{1}{\lambda }=R_H\times Z^2[\frac{1}{1^2}-\frac{1}{3^2}]$ $(\because Z=3$ for $Li)$
$=109678\times 3^2\times \left[8/9\right]$
$\therefore \lambda =1.14\times {10}^{-6}cm$