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(D) The radius of the $n$-th orbit in a hydrogen atom is given by the formula $r_n = n^2 r_1$, where $r_1$ is the radius of the first orbit (Bohr radi

Vedclass · Accepted Answer

$4.77 	imes 10^{-10} 	ext{ m}$

Vedclass · Answer

(D) The radius of the $n$-th orbit in a hydrogen atom is given by the formula $r_n = n^2 r_1$, where $r_1$ is the radius of the first orbit (Bohr radius).Given $r_1 = 5.3 	imes 10^{-11} 	ext{ m}$ and $n = 3$.Substituting these values into the formula:$r_3 = 3^2 	imes (5.3 	imes 10^{-11} 	ext{ m})$$r_3 = 9 	imes 5.3 	imes 10^{-11} 	ext{ m}$$r_3 = 47.7 	imes 10^{-11} 	ext{ m}$$r_3 = 4.77 	imes 10^{-10} 	ext{ m}$.Thus, the radius of the $n = 3$ orbit is $4.77 	imes 10^{-10} 	ext{ m}$.Therefore, the correct option is $D$.

The radius of the innermost electron orbit of a hydrogen atom is $5.3 \times 10^{-11} \text{ m}$. What is the radius of the $n = 3$ orbit?

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