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Question

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

Vedclass · Accepted Answer

$4$

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(B) The radius of the $n^{th}$ orbit of a hydrogen-like atom is given by the formula: $r_n = r_0 \frac{n^2}{Z}$, where $r_0$ is the radius of the first Bohr orbit of hydrogen $(0.5 \ \mathring{A})$, $n$ is the principal quantum number, and $Z$ is the atomic number.For the third excited state of $He^+$, the principal quantum number is $n = 3 + 1 = 4$.The atomic number of Helium is $Z = 2$.Substituting these values into the formula:$r_4 = 0.5 	imes \frac{4^2}{2} = 0.5 	imes \frac{16}{2} = 0.5 	imes 8 = 4 \ \mathring{A}$.Thus, the correct option is $B$.

The radius of the Bohr orbit in the ground state of a hydrogen atom is $0.5 \ \mathring{A}$. The radius of the orbit of the electron in the third excited state of $He^+$ will be ...... $\mathring{A}$.

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