The ratio of radii of the second orbit of a h | vedclass

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Question

(C) For hydrogen and hydrogen-like atoms,the radius of the $n^{th}$ orbit is given by the formula: $r_n \propto \frac{n^2}{Z}$,where $n$ is the orbit

Vedclass · Accepted Answer

$1: 2$

Vedclass · Answer

(C) For hydrogen and hydrogen-like atoms,the radius of the $n^{th}$ orbit is given by the formula: $r_n \propto \frac{n^2}{Z}$,where $n$ is the orbit number and $Z$ is the atomic number.For a hydrogen atom $(H)$,$Z = 1$. The radius of the second orbit $(n = 2)$ is $r_2 = \frac{2^2}{1} = 4$.For a helium ion $(He^{+})$,$Z = 2$. The radius of the fourth orbit $(n = 4)$ is $r_4 = \frac{4^2}{2} = \frac{16}{2} = 8$.The ratio of the radii is $\frac{r_2}{r_4} = \frac{4}{8} = \frac{1}{2}$,which is $1: 2$.

The ratio of radii of the second orbit of a hydrogen atom to the fourth orbit of a $He^{+}$ ion is:

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