The radius of a hydrogen atom in its ground s | vedclass

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

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$0.176$

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(A) The radius of an orbit for a hydrogen-like species is given by the formula $r_n = 0.529 	imes \frac{n^2}{Z} \ \mathring{A}$.
For the ground state,$n = 1$.
For a hydrogen atom,$Z = 1$,so $r_H = 0.529 	imes \frac{1^2}{1} = 0.529 \ \mathring{A} \approx 0.53 \ \mathring{A}$.
For the $Li^{2+}$ ion,$Z = 3$,so $r_{Li^{2+}} = 0.529 	imes \frac{1^2}{3} = \frac{0.529}{3} \ \mathring{A} \approx 0.176 \ \mathring{A}$.

The radius of a hydrogen atom in its ground state is $0.53 \ \mathring{A}$. The radius of the $Li^{2+}$ ion in the same state (atomic number = $3$) is ............. $\mathring{A}$.

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