Question

What is the smallest wavelength observed in the spectra of $L{i}^{2+}$?

• A. $8.6nm$
• B. $10.4nm$
• C. $12.8nm$
• D. $14.6nm$

Answer 1

The correct option is B $10.4nm$

Given, both absorb $10.2eV$.
Consider ${Li}^{2+}$, Its energy levels are $-122.4eV,-30.6eV,-13.6eV,-7.65eV,-4.896eV,-3.4eV,-2.49eV,1.91eV$.........
Possible transition is from $n=3$ to $n=6$
When de excited, ${Li}^{2+}$ gives $\frac{6\times 5}{2}=15lines$
In these lines, smallest wavelength corresponds to the line from $n=6$ to $n=1$.
$\frac{1}{\lambda }=(1.097\times {10}^7)\left(9\right)(1-\frac{1}{36})=9.6\times {10}^7\Rightarrow \lambda =10.4\times {10}^{-9}m$