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Physics - Modern Physics Question with Solution | TestHub

PhysicsModern PhysicsAtomic structureMedium2 minQB

PhysicsMediumnumerical

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 $n^{\frac{1}{α}}$ , where $α$ is _______ .

Answer:

3.00

Solution:

$F = \frac{- d U}{d r} = - 4 U_{0} r^{3} = \frac{m v ^{2}}{r}$

$m v^{2} = 4 U_{0} r^{4}$

$V \propto r^{2}$

$r^{3} \propto n$

$\Rightarrow r \propto n^{1/3}$ $= 3$

Stream:JEESubject:PhysicsTopic:Modern PhysicsSubtopic:Atomic structure

⏱ 2mℹ️ Source: QB

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