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(B) The energy of an electron in a hydrogen-like species is given by $E_n = -13.6 	imes \frac{Z^2}{n^2} 	ext{ eV}$.
For the same excited state,$n$

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$3: 1$

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(B) The energy of an electron in a hydrogen-like species is given by $E_n = -13.6 	imes \frac{Z^2}{n^2} 	ext{ eV}$.
For the same excited state,$n$ is constant,so $E \propto Z^2$.
Given the ratio of energies $\frac{E_H}{E_{Li^{2+}}} = \frac{1}{9}$,we have $\frac{Z_H^2}{Z_{Li^{2+}}^2} = \frac{1^2}{3^2} = \frac{1}{9}$,which is consistent with the given data.
The radius of an electron in a hydrogen-like species is given by $r_n = 0.529 	imes \frac{n^2}{Z} \mathring{A} $.
For the same excited state,$n$ is constant,so $r \propto \frac{1}{Z}$.
Therefore,the ratio of radii is $\frac{r_H}{r_{Li^{2+}}} = \frac{Z_{Li^{2+}}}{Z_H} = \frac{3}{1} = 3: 1$.

If the ratio of energies of an electron in the excited states of $H$ and $Li^{2+}$ is $1: 9$,the radius ratio of the electron in the same excited states of $H$ and $Li^{2+}$ is

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