Q52 / 75 · JEE Main 2025 (4 Apr Shift 1) · Physics
Considering the Bohr model of hydrogen like atoms, the ratio of the ratio of the radius $5^{\text {th }}$ orbit of the electron in $\mathrm{Li}^{2+}$ and $\mathrm{He}^{+}$is
- A$\frac{3}{2}$
- B$\frac{4}{9}$
- C$\frac{9}{4}$
- Correct answerD$\frac{2}{3}$
Solution
$\mathrm{r}=\mathrm{r} \cdot \frac{\mathrm{n}^2}{2}$
for $\mathrm{Li}^{2+}$
$r_5=r \cdot \frac{25}{3}$
for $\mathrm{He}^{+}$
$\begin{aligned}<br/>& \mathrm{r}_5=\mathrm{r} \cdot \frac{25}{2} \\ & \therefore \frac{\mathrm{r}_{\mathrm{Li}^{2+}}}{\mathrm{r}_{\mathrm{He}^{+}}}=\frac{2}{3}<br/>\end{aligned}$
for $\mathrm{Li}^{2+}$
$r_5=r \cdot \frac{25}{3}$
for $\mathrm{He}^{+}$
$\begin{aligned}<br/>& \mathrm{r}_5=\mathrm{r} \cdot \frac{25}{2} \\ & \therefore \frac{\mathrm{r}_{\mathrm{Li}^{2+}}}{\mathrm{r}_{\mathrm{He}^{+}}}=\frac{2}{3}<br/>\end{aligned}$
Hence, the correct answer is option: 'D'.