The radii of the first four Bohr orbits of th | vedclass

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(B) According to Bohr's model, the radius of the $n^{th}$ orbit of a hydrogen atom is given by the formula $r_n = a_0 n^2$, where $a_0$ is the Bohr ra

Vedclass · Accepted Answer

$1: 4: 9: 16$

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(B) According to Bohr's model, the radius of the $n^{th}$ orbit of a hydrogen atom is given by the formula $r_n = a_0 n^2$, where $a_0$ is the Bohr radius and $n$ is the principal quantum number.This implies that the radius $r$ is directly proportional to the square of the principal quantum number, i.e., $r \propto n^2$.For the first four orbits $(n = 1, 2, 3, 4)$, the radii are proportional to $1^2, 2^2, 3^2, 4^2$.Calculating these values, we get $1: 4: 9: 16$.Therefore, the correct option is $B$.

The radii of the first four Bohr orbits of the hydrogen atom are related as:

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