The radius of the 2^{nd} orbit of Li^{2+} is | vedclass

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(C) The radius of an orbit in a hydrogen-like species is given by $r_n = a_0 	imes \frac{n^2}{Z}$,where $n$ is the orbit number and $Z$ is the atomic

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$\frac{27}{16} x$

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(C) The radius of an orbit in a hydrogen-like species is given by $r_n = a_0 	imes \frac{n^2}{Z}$,where $n$ is the orbit number and $Z$ is the atomic number.For $Li^{2+}$,$Z = 3$ and $n = 2$. Given $r_2 = x$,we have $x = a_0 	imes \frac{2^2}{3} = \frac{4a_0}{3}$,which implies $a_0 = \frac{3x}{4}$.For $Be^{3+}$,$Z = 4$ and $n = 3$. The radius $r_3$ is $r_3 = a_0 	imes \frac{3^2}{4} = \frac{9a_0}{4}$.Substituting $a_0 = \frac{3x}{4}$ into the expression for $r_3$:$r_3 = \frac{9}{4} 	imes (\frac{3x}{4}) = \frac{27}{16} x$.

The radius of the $2^{nd}$ orbit of $Li^{2+}$ is $x$. The expected radius of the $3^{rd}$ orbit of $Be^{3+}$ is:

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