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JEE Main 202117 MarchEvening Shift

Exam: JEE Main
Year: 2021
Date: 17 March
Shift: Evening Shift
Subject: Physics
Chapter: Atomic Physics

JEE Main 2021 · 17 March · Evening Shift · Physics · Atomic Physics

A particle of mass m moves in a circular orbit in a central...

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\dfrac{1}{\alpha}

, where

\alpha

is _______ .

Correct answer

0

Step-by-step solution

$F = \dfrac{- dU}{dr} = - 4{U}_{0}{r}^{3} = \dfrac{m{v}^{2}}{r}$

$m{v}^{2} = 4{U}_{0}{r}^{4}$

$V ∝ {r}^{2}$

${r}^{3} ∝ n$

$⇒ r ∝ {n}^{1 / 3}$ $= 3$

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