The radius of the 2 nd orbit of Li 2 + is x . The expected radius of the 3 rd orbit of Be 3 + is [2023]

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Solution

Q.
The radius of the $2^{nd}$ orbit of ${Li}^{2 +}$ is $x$ . The expected radius of the $3^{rd}$ orbit of ${Be}^{3 +}$ is [2023]

1 $\frac{16}{27} x$

2 $\frac{4}{9} x$

3 $\frac{9}{4} x$

4 $\frac{27}{16} x$

Ans.
(4)

$R = 0.529 \times \frac{n^{2}}{Z}$

${(r_{{Li}^{2 +}})}_{n = 2} = 0.529 \times \frac{{(2)}^{2}}{3} = x$

${(r_{{Be}^{3 +}})}_{n = 3} = 0.529 \times \frac{{(3)}^{2}}{4}$

$\frac{{(r_{{Li}^{2 +}})}_{n = 2}}{{(r_{{Be}^{3 +}})}_{n = 3}} = \frac{\frac{r_{0} \times {(2)}^{2}}{3}}{\frac{r_{0} \times {(3)}^{2}}{4}}$

$\frac{x}{{(r_{{Be}^{3 +}})}_{n = 3}} = \frac{16}{27}$

${(r_{{Be}^{3 +}})}_{n = 3} = \frac{27 x}{16}$

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