Question

One of the lines in the emission spectrum of $Li ^{2+}$ 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 $n =12 \rightarrow n = x$. 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 $Li ^{2+}\left[\frac{1}{\lambda}= R \times 9\left(\frac{1}{ x ^{2}}-\frac{1}{12^{2}}\right)=\frac{3 R }{16}\right]$
which is satisfied by $n =12 \rightarrow n =6$.