Question

One of the lines in the emission spectrum of $L{i}^{2+}$ has the same wavelength as that of the $2^{\text{nd }}$ line of Balmer series in hydrogen spectrum. The electronic transition corresponding to this line is $n=12\to n=x$. Find the value of $x$.

• A. 8
• B. 6
• C. 7
• D. 5

Answer 1

Answer: (B)

For $2^{\text{nd }}$ line of Balmer series in hydrogen spectrum
$\frac{1}{\lambda }=R(1)\left(\frac{1}{2^2}-\frac{1}{4^2}\right)$
$=\frac{3}{16}R$
For $L{i}^{2+}\left[\frac{1}{\lambda }=R\times 9\left(\frac{1}{x^2}-\frac{1}{12^2}\right)=\frac{3R}{16}\right]$
which is satisfied by $n=12\to n=6$.