JEE Mains · Physics · STD 12 - 12. atoms
A particle of mass \(m\) moves in a circular orbit in a central potential field \(U ( r )= U _{0} r ^{4}\). If Bohr's quantization conditions are applied, radii of possible orbitals \(r _{ n }\) vary with \(n ^{1 / \alpha}\), where \(\alpha\) is ....... .
- A \(6\)
- B \(9\)
- C \(3\)
- D \(4\)
Answer & Solution
Correct Answer
(C) \(3\)
Step-by-step Solution
Detailed explanation
\(F =\frac{- d U }{ dr }=-4 U _{0} r ^{3}=\frac{ mv ^{2}}{ r }\) \(mv ^{2}=4 U _{0} r ^{4}\) \(v \propto r ^{2}\) \(mvr =\frac{ nh }{2 \pi}\) \(r ^{3} \propto n\) \(r \propto n^{1 / 3}\) \(\alpha=3\)
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