KCET · Physics · Atomic Physics
The period of revolution of an electron revolving in nth orbit of H-atom is proportional to
- A \(n^{2}\)
- B \(\frac{1}{n}\)
- C \(n^{3}\)
- D independent of \(n\)
Answer & Solution
Correct Answer
(C) \(n^{3}\)
Step-by-step Solution
Detailed explanation
The time period of revolution of an electron revolving in \(n\)th orbit of \(\mathrm{H}\)-atom is given by
\(\begin{array}{ll}
& T_{n}=\frac{2 \pi r_{n}}{v_{n}}=\left(\frac{4 \varepsilon_{0}^{2} h^{2}}{m e^{4}}\right) \frac{n^{3}}{z^{2}} \\
\Rightarrow \quad & T_{n} \propto n^{3}
\end{array}\)
\(\begin{array}{ll}
& T_{n}=\frac{2 \pi r_{n}}{v_{n}}=\left(\frac{4 \varepsilon_{0}^{2} h^{2}}{m e^{4}}\right) \frac{n^{3}}{z^{2}} \\
\Rightarrow \quad & T_{n} \propto n^{3}
\end{array}\)
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