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(D) According to Bohr's atomic model, the radius $r$ is given by $r \propto \frac{n^2}{Z}$.For the $3^{rd}$ orbit of $Li^{2+}$, $n_1 = 3$ and $Z_1 = 3

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$158.7 \, pm$

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(D) According to Bohr's atomic model, the radius $r$ is given by $r \propto \frac{n^2}{Z}$.For the $3^{rd}$ orbit of $Li^{2+}$, $n_1 = 3$ and $Z_1 = 3$.For the $2^{nd}$ orbit of $He^{+}$, $n_2 = 2$ and $Z_2 = 2$.Using the ratio formula: $\frac{(r_3)_{Li^{2+}}}{(r_2)_{He^{+}}} = \frac{n_1^2}{n_2^2} 	imes \frac{Z_2}{Z_1}$.Substituting the values: $\frac{(r_3)_{Li^{2+}}}{105.8 \, pm} = \frac{3^2}{2^2} 	imes \frac{2}{3} = \frac{9}{4} 	imes \frac{2}{3} = \frac{3}{2} = 1.5$.Therefore, $(r_3)_{Li^{2+}} = 105.8 \, pm 	imes 1.5 = 158.7 \, pm$.

If the radius of the second Bohr orbit of the $He^{+}$ ion is $105.8 \, pm$, what is the radius of the third Bohr orbit of the $Li^{2+}$ ion?

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