MHT CET · Physics · Atomic Physics
Ratio of centripetal acceleration for an electron revolving in \(3^{\text {rd }}\) orbit and \(5^{\text {th }}\) Bohr orbit of hydrogen atom is
- A \(\frac{125}{81}\)
- B \(\frac{625}{81}\)
- C \(\frac{625}{27}\)
- D \(\frac{25}{9}\)
Answer & Solution
Correct Answer
(B) \(\frac{625}{81}\)
Step-by-step Solution
Detailed explanation
Centripetal acceleration \(a=\frac{v^2}{r}\)
In Bohr orbit, the velocity \(v \propto \frac{1}{n}\) and radius \(r \propto n^2\) have functional dependencies on orbit number \(n\).
Thus, the centripetal acceleration depends on the orbit number as follows: \(a \propto \frac{1}{n^4}\)
\(\therefore \frac{a_3}{a_5}=\frac{5^4}{3^4}=\frac{625}{81}\)
In Bohr orbit, the velocity \(v \propto \frac{1}{n}\) and radius \(r \propto n^2\) have functional dependencies on orbit number \(n\).
Thus, the centripetal acceleration depends on the orbit number as follows: \(a \propto \frac{1}{n^4}\)
\(\therefore \frac{a_3}{a_5}=\frac{5^4}{3^4}=\frac{625}{81}\)
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