Find the radius of the first,second,and third | vedclass

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Question

(A) The radius of the $n^{th}$ orbit of a hydrogen-like atom is given by the formula: $r_n = a_0 	imes n^2 / Z$,where $a_0 = 0.0529 \ nm$ and $Z = 1$

Vedclass · Accepted Answer

$0.0529 \ nm, 0.2116 \ nm, 0.4761 \ nm$

Vedclass · Answer

(A) The radius of the $n^{th}$ orbit of a hydrogen-like atom is given by the formula: $r_n = a_0 	imes n^2 / Z$,where $a_0 = 0.0529 \ nm$ and $Z = 1$ for hydrogen.For the first orbit $(n=1)$: $r_1 = 0.0529 	imes (1)^2 / 1 = 0.0529 \ nm$.For the second orbit $(n=2)$: $r_2 = 0.0529 	imes (2)^2 / 1 = 0.0529 	imes 4 = 0.2116 \ nm$.For the third orbit $(n=3)$: $r_3 = 0.0529 	imes (3)^2 / 1 = 0.0529 	imes 9 = 0.4761 \ nm$.

Find the radius of the first,second,and third orbits of the hydrogen atom.

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