The approximate value of principal quantum number for a circular orbit of hydrogen atom of radius $530…

The approximate value of principal quantum number for a circular orbit of hydrogen atom of radius $530 \mathrm{~nm}$ is
  1. 26
  2. 100
  3. 200
  4. 21

Solution

Radius of electron of hydrogen in $n^{\text {th }}$ orbit, $\begin{aligned} & r_n=n^2 \times 0.53 Å \\ & 530 \mathrm{~nm}=n^2 \times 0.053 Å \\ & \therefore \quad 530 \times 10^{-9} \mathrm{~m}=n^2 \times 0.53 \times 10^{-10} \mathrm{~m} \\ & \Rightarrow \quad n^2=\frac{5300}{0.53} \\ & \Rightarrow \quad n^2=10^4 \\ & n=100 \\ & \end{aligned}$

Asked in: AP EAMCET 2018 (24 Apr Shift 1)

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