What is the radius of the fourth orbit of hydrogen atom?

What is the radius of the fourth orbit of hydrogen atom?
  1. $846.4 \mathrm{pm}$
  2. $211.6 \mathrm{pm}$
  3. $476.1 \mathrm{pm}$
  4. $1322.5 \mathrm{pm}$

Solution

$\mathrm{r}_{\mathrm{n}}=\frac{52.9(\mathrm{n})^2}{\mathrm{Z}} \mathrm{pm}$ For hydrogen, $Z=1$ $r_n=\frac{52.9 \times 4^2}{1}=846.4 \mathrm{pm}$

Asked in: MHT CET 2023 (12 May Shift 2)

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