The radius ratio of Bohr's first orbit of | vedclass

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(C) 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 f

Vedclass · Accepted Answer

$6: 4: 3$

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(C) 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 first orbit,$n = 1$,so $r_1 \propto \frac{1}{Z}$.
For $He^{+}$ $(Z = 2)$,$r_{He^+} \propto \frac{1}{2}$.
For $Li^{2+}$ $(Z = 3)$,$r_{Li^{2+}} \propto \frac{1}{3}$.
For $Be^{3+}$ $(Z = 4)$,$r_{Be^{3+}} \propto \frac{1}{4}$.
The ratio is $\frac{1}{2} : \frac{1}{3} : \frac{1}{4}$.
To simplify,multiply by the least common multiple of $2, 3, 4$,which is $12$.
Ratio $= (\frac{1}{2} 	imes 12) : (\frac{1}{3} 	imes 12) : (\frac{1}{4} 	imes 12) = 6 : 4 : 3$.

The radius ratio of Bohr's first orbit of hydrogen-like species $He^{+}$,$Li^{2+}$,and $Be^{3+}$ is:

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