Question

Calculate the wavelength of the spectral line obtained in the spectrum of $L{i}^{2+}$ ion when the transition takes place between two levels whose sum is $4$ and difference is $2$.

• A. $1.64\times 10^{-8}m$
• B. $1.18\times 10^{-8}m$
• C. $1.80\times 10^{-8}m$
• D. $1.39\times 10^{-8}m$

Answer 1

Answer: (D)

Given that: $n_1+n_2=4$ and $n_2-n_1=2$
Solving these equations, we get $n_1=1,n_2=3$
Hence, $\frac{1}{\lambda }=R{Z}^2\left(\frac{1}{n_1^2}-\frac{1}{n_2^2}\right)$
$\frac{1}{\lambda }=1.0967\times 10^7\times 9\left(\frac{1}{1}-\frac{1}{9}\right)M^{-1}$
or $\lambda =1.39\times 10^{-8}\mathrm{m}$