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QJEEM23Chb645: JEE Main 2023 Chemistry - Class 11 JEEM23Chb645 Solution: The radius of the orbit of is . The expected radius of the…

The radius of the $\mathrm{2^{nd}}$ orbit of $\mathrm{Li^{2+}}$ is $x$ . The expected radius of the $\mathrm{3^{rd}}$ orbit of $\mathrm{Be^{3+}}$ is

Multiple Choice Options

A $\frac{16}{27}x$
B $\frac{4}{9}x$
C $\frac{9}{4}x$
D $\frac{27}{16}x$

Step-by-Step Verified Solution

r_{\mathrm{Li}^{+}}=r_{0} \times \frac{2^{2}}{3}=x \Rightarrow r_{0}=\frac{3 x}{4}

\mathrm{r}_{\mathrm{Be}^{3+}}=\mathrm{r}_{0} \times \frac{3^{2}}{4}

r_{\mathrm{Be}^{3+}}=\frac{3 \mathrm{x}}{4} \times \frac{3^{2}}{4}=\frac{27 \mathrm{x}}{16}

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