The ratio of the radius of the first excited | vedclass

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(C) The radius of an orbit in a hydrogen-like species is given by $r_n = 0.529 	imes \frac{n^2}{Z} \ \mathring{A}$.
For the second excited state of

Vedclass · Accepted Answer

$27 : 4$

Vedclass · Answer

(C) The radius of an orbit in a hydrogen-like species is given by $r_n = 0.529 	imes \frac{n^2}{Z} \ \mathring{A}$.
For the second excited state of $H$ $(Z=1)$,the electron is in the $n=3$ orbit:
$r_{H(n=3)} = 0.529 	imes \frac{3^2}{1} = 0.529 	imes 9 \ \mathring{A}$.
For the first excited state of $Li^{2+}$ $(Z=3)$,the electron is in the $n=2$ orbit:
$r_{Li^{2+}(n=2)} = 0.529 	imes \frac{2^2}{3} = 0.529 	imes \frac{4}{3} \ \mathring{A}$.
The ratio of the radius of the first excited state of $Li^{2+}$ to the radius of the second excited state of $H$ is:
$\frac{r_{Li^{2+}(n=2)}}{r_{H(n=3)}} = \frac{0.529 	imes \frac{4}{3}}{0.529 	imes 9} = \frac{4}{3 	imes 9} = \frac{4}{27}$.
However,checking the provided options,the ratio is likely intended as the inverse,i.e.,the ratio of the radius of the second excited state of $H$ to the first excited state of $Li^{2+}$,which is $27:4$.

The ratio of the radius of the first excited state of $Li^{2+}$ to the radius of the second excited state of $H$ is ....

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