Exam

JEE Main

Year

2015

Date

10 April

Mode

Online

Subject

Physics

Chapter

Atomic Physics

JEE Main 2015 · 10 April · Online · Physics · Atomic Physics

If one were to apply the Bohr model to a particle of mass ' m ' and...

If one were to apply the Bohr model to a particle of mass $' m '$ and charge $' q '$ moving in a plane under the influence of a magnetic field 'B', the energy of the charged particle in the ${n}^{th}$ level will be:

Step-by-step solution

For a charge $q$ moving in a uniform magnetic field $B$



${f}_{m} = \dfrac{m{v}^{2}}{R}$

$qVB = \dfrac{m{v}^{2}}{R}$

$⇒ m{v}^{2} = qVBR$

$⇒ \dfrac{1}{2}m{v}^{2} = \dfrac{qVBR}{2}$

$⇒ Energy = \dfrac{qVBR}{2} ( 1 )$

By Bohr's quantization condition,

Angular momentum $L = n\dfrac{h}{2\pi}$

$⇒ mvR = \dfrac{nh}{2\pi}$

$⇒ vR = \dfrac{nh}{2\pim} ( 2 )$

Put $( 2 )$ in $( 1 )$

$⇒ Energy = \dfrac{qB}{2}\left(\dfrac{nh}{2\pim}\right)$

$= \dfrac{qBnh}{4\pim}$