In the hydrogen atom, the radii of the first | vedclass

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(A) The radius of the $n^{th}$ Bohr orbit in a hydrogen atom is given by the formula: $r_n = n^2 a_0$ where $n$ is the principal quantum number $(n =

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$1 : 4 : 9 : 16$

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(A) The radius of the $n^{th}$ Bohr orbit in a hydrogen atom is given by the formula: $r_n = n^2 a_0$ where $n$ is the principal quantum number $(n = 1, 2, 3, 4, ...)$ and $a_0$ is the Bohr radius. For the first four orbits: For $n = 1$, $r_1 = 1^2 a_0 = 1 a_0$ For $n = 2$, $r_2 = 2^2 a_0 = 4 a_0$ For $n = 3$, $r_3 = 3^2 a_0 = 9 a_0$ For $n = 4$, $r_4 = 4^2 a_0 = 16 a_0$ Thus, the ratio of the radii is $r_1 : r_2 : r_3 : r_4 = 1 : 4 : 9 : 16$.

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

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