The radius of the first orbit of $\mathrm{Li}^{2+}$ is $\mathrm{X} Å$. The radius of the third orbit of…
The radius of the first orbit of $\mathrm{Li}^{2+}$ is $\mathrm{X} Å$. The radius of the third orbit of $\mathrm{He}^{+}$(in $Å$ ) is
- $\frac{18}{2} x$
- $\frac{18}{3} x$
- $\frac{27}{4} x$
- $\frac{27}{2} x$
Solution
Radius of 1st Bohr orbit, $\mathrm{r}=\frac{0.529 \mathrm{n}^2}{\mathrm{z}} Å$
$\begin{aligned} & \therefore \mathrm{r}_{\mathrm{He}^{+}}: \mathrm{r}_{\mathrm{Li}^{2+}}=\frac{0.529 \times 3^2}{2}: \frac{0.529 \times 1^2}{3}=\frac{9}{2}: \frac{1}{3} \\ & \therefore \mathrm{r}_{\mathrm{He}^{+}}=\frac{27}{2} x\end{aligned}$
Asked in: AP EAMCET 2022 (08 Jul Shift 1)
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