The radius of inner most orbit of hydrogen atom is $5.3 imes 10^{-11} ext{ m}$. What is the radius of thir

Question

The radius of inner most orbit of hydrogen atom is $5.3 	imes 10^{-11} 	ext{ m}$. What is the radius of third allowed orbit of hydrogen atom?

Accepted Answer

The radius of the $n$-th orbit of a hydrogen atom is given by $r_n = n^2 r_1$, where $r_1 = 5.3 	imes 10^{-11} 	ext{ m} = 0.53 	ext{ } 	ext{\AA}$. For the third orbit, $n = 3$, so $r_3 = 3^2 	imes 0.53 	ext{ } 	ext{\AA} = 9 	imes 0.53 	ext{ } 	ext{\AA} = 4.77 	ext{ } 	ext{\AA}$.

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