Atoms & Nuclei

JEE Main level, single correct, medium

34 of 239

Question 34 of 239

Considering the Bohr model of hydrogen like atoms, the ratio of the ratio of the radius 5th 5^{\text {th }} orbit of the electron in Li2+\mathrm{Li}^{2+} and He+\mathrm{He}^{+}is

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Answer: (D) 23\frac{2}{3}

r=r⋅n22\mathrm{r}=\mathrm{r} \cdot \frac{\mathrm{n}^2}{2}
for Li2+\mathrm{Li}^{2+}
r5=r⋅253r_5=r \cdot \frac{25}{3}
for He+\mathrm{He}^{+}
$\begin{aligned}
& \mathrm{r}_5=\mathrm{r} \cdot \frac{25}{2} \\
& \therefore \frac{\mathrm{r}_{\mathrm{Li}^{2+}}}{\mathrm{r}_{\mathrm{He}^{+}}}=\frac{2}{3}
\end{aligned}$

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