Question

Calculate the wavelength of the spectral line obtained in the spectrum of $Li^{2+}$ 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. $1 .1 8 \times 10^{-8} m$
• 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 $\lambda=1.39 \times 10^{-8} \mathrm{~m}$