JEE Mains · Physics · STD 12 - Atoms
- JEE Mains 2021
- Hard
- Numerical
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 ....... .
Pick an option to check your answer.
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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