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Question: Answered & Verified by Expert
According to Bohr's theory, which of the following correctly represents the variation of energy and radius of an electron in $n^{\text {th }}$ orbit of $\mathrm{H}$-atom?
ChemistryStructure of AtomAIIMSAIIMS 2016
Options:
  • A $E_n \propto \frac{1}{n^2}, r \propto \frac{1}{n^2}$
  • B $E_n \propto \frac{1}{n^2}, r \propto n^2$
  • C $E_n \propto n^2, r \propto n^2$
  • D $E_n \propto n, r \propto \frac{1}{n}$
Solution:
2161 Upvotes Verified Answer
The correct answer is: $E_n \propto \frac{1}{n^2}, r \propto n^2$
According to Bohr's theory,
$r=\frac{n^2 h^2}{4 \pi^2 m Z e^2 k}$ and $E_n=\frac{-k^2 2 \pi^2 m Z^2 e^4}{n^2 h^2}$

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