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(B) The radius of the $n^{th}$ orbit in a hydrogen-like atom is given by the formula: $r_n = r_0 	imes \frac{n^2}{Z}$, where $r_0 = 0.53 \ \mathring{

Vedclass · Accepted Answer

$1.06$

Vedclass · Answer

(B) The radius of the $n^{th}$ orbit in a hydrogen-like atom is given by the formula: $r_n = r_0 	imes \frac{n^2}{Z}$, where $r_0 = 0.53 \ \mathring{A}$ is the radius of the first orbit of the hydrogen atom.For a helium ion $(He^+)$, the atomic number $Z = 2$.For the second orbit, $n = 2$.Substituting these values into the formula:$r_2 = 0.53 	imes \frac{2^2}{2} \ \mathring{A}$$r_2 = 0.53 	imes \frac{4}{2} \ \mathring{A}$$r_2 = 0.53 	imes 2 \ \mathring{A} = 1.06 \ \mathring{A}$.Thus, the correct option is $B$.

According to Bohr's model, the radius of the second orbit of a helium ion $(He^+)$ is ........ $\mathring{A}$.

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