Which of the following is radius of first orbit of $\mathrm{He}^{+}$?
Which of the following is radius of first orbit of $\mathrm{He}^{+}$?
52.90 pm
78.90 pm
26.45 pm
13.35 pm
Solution
Radius of $\mathrm{n}^{\text {th }}$ orbit $=\mathrm{r}_{\mathrm{n}}=\frac{52.9 \times(\mathrm{n})^2}{\mathrm{Z}} \mathrm{pm}$
$\mathrm{He}^{+}$is a hydrogen-like species having $\mathrm{Z}=2$.
Radius of the first orbit of $\mathrm{He}^{+}$
$\begin{aligned}
& =\mathrm{r}_1 \\
& =\frac{52.9 \times(1)^2}{2} \mathrm{pm} \\
& =26.45 \mathrm{pm}
\end{aligned}$