The radius of which of the following orbits i | vedclass

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(D) The radius of the $n^{th}$ orbit of a hydrogen-like species is given by the formula: $r_n = 0.529 	imes \frac{n^2}{Z} \ \mathring{A}$.For the $1^

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$Be^{3+} \ (n = 2)$

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(D) The radius of the $n^{th}$ orbit of a hydrogen-like species is given by the formula: $r_n = 0.529 	imes \frac{n^2}{Z} \ \mathring{A}$.For the $1^{st}$ orbit of $H$ atom,$n=1$ and $Z=1$,so $r_H = 0.529 	imes \frac{1^2}{1} = 0.529 \ \mathring{A}$.Checking the options:$A$: For $He^{+} \ (n=2, Z=2)$,$r = 0.529 	imes \frac{2^2}{2} = 0.529 	imes 2 = 1.058 \ \mathring{A}$.$B$: For $Li^{2+} \ (n=2, Z=3)$,$r = 0.529 	imes \frac{2^2}{3} = 0.529 	imes \frac{4}{3} = 0.705 \ \mathring{A}$.$C$: For $Li^{2+} \ (n=3, Z=3)$,$r = 0.529 	imes \frac{3^2}{3} = 0.529 	imes 3 = 1.587 \ \mathring{A}$.$D$: For $Be^{3+} \ (n=2, Z=4)$,$r = 0.529 	imes \frac{2^2}{4} = 0.529 	imes 1 = 0.529 \ \mathring{A}$.Thus,the radius of $Be^{3+} \ (n=2)$ is the same as that of the $1^{st}$ orbit of $H$ atom.

The radius of which of the following orbits is the same as that of the $1^{st}$ orbit of $H$ atom?

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