Chemistry - Atomic Structure Question with Solution | TestHub

For a one-electron ion, $Z=2$, and

$$\frac{1}{\lambda }=R{Z}^2\left(\frac{1}{1^2}-\frac{1}{2^2}\right)=R\cdot 4\cdot \frac{3}{4}=3R.$$

Hence $\lambda =(1/R)/3=911.7/3=303.90\mathring{\mathrm{A}}$.

*Editorial correction:* the question PDF says $\mathrm{H}{\mathrm{e}}^{2+}$. That is a bare helium nucleus with no electron to excite. The supplied solution uses $Z=2$ for a one-electron ion, so the intended species is $\mathrm{H}{\mathrm{e}}^{+}$.