Circumference of the first orbit of hydrogen | vedclass

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Question

(A) The circumference of an orbit is given by the formula $C = 2 \pi r$.For the hydrogen atom,the radius of the $n^{th}$ orbit is given by $r_n = n^2

Vedclass · Accepted Answer

$2 \pi \alpha _0$

Vedclass · Answer

(A) The circumference of an orbit is given by the formula $C = 2 \pi r$.For the hydrogen atom,the radius of the $n^{th}$ orbit is given by $r_n = n^2 \alpha _0$,where $\alpha _0$ is the Bohr radius.For the first orbit $(n = 1)$,the radius is $r = 1^2 	imes \alpha _0 = \alpha _0$.Substituting this into the circumference formula,we get $C = 2 \pi \alpha _0$.Since $\sqrt{4} = 2$,the expression can also be written as $C = \sqrt{4} \pi \alpha _0$.

Circumference of the first orbit of hydrogen atom is given by the formula :

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