Bohr model is applied to a particle of mass m | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(A) According to the Bohr quantization condition,the angular momentum is given by $mvr = \frac{nh}{2 \pi}$.Therefore,$vr = \frac{nh}{2 \pi m} \dots (i

Vedclass · Accepted Answer

$\frac{nhqB}{4 \pi m}$

Vedclass · Answer

(A) According to the Bohr quantization condition,the angular momentum is given by $mvr = \frac{nh}{2 \pi}$.Therefore,$vr = \frac{nh}{2 \pi m} \dots (i)$.For a particle moving in a circular path under a magnetic field,the magnetic force provides the centripetal force: $qvB = \frac{mv^2}{r}$.This simplifies to $mv = qBr$,or $v = \frac{qBr}{m} \dots (ii)$.Substituting $v$ from $(ii)$ into $(i)$,we get $(\frac{qBr}{m})r = \frac{nh}{2 \pi m}$,which implies $r^2 = \frac{nh}{2 \pi qB}$.The kinetic energy $E$ is given by $E = \frac{1}{2}mv^2$. Since $mv = qBr$,we have $E = \frac{1}{2}m(\frac{qBr}{m})^2 = \frac{q^2 B^2 r^2}{2m}$.Substituting $r^2$ into the energy expression: $E = \frac{q^2 B^2}{2m} 	imes \frac{nh}{2 \pi qB} = \frac{nhqB}{4 \pi m}$.

Bohr model is applied to a particle of mass $m$ and charge $q$ moving in a plane under the influence of a transverse magnetic field $B$. The energy of the charged particle in the $n^{\text{th}}$ level will be $[h = \text{Planck's constant}]$

Similar Questions

$A$ proton beam enters a magnetic field of $ 10^{-4} \,Wb m^{-2} $ normally. If the specific charge of the proton is $ 10^{11} \,C kg^{-1} $ and its velocity is $ 10^{9} \,ms^{-1} $, then the radius of the circle described will be (in $\,m$)

If a charge is moving parallel or antiparallel to a magnetic field,what is the magnetic force acting on it?

An electron is moving along the positive $X$-axis. You want to apply a magnetic field for a short time so that the electron may reverse its direction and move parallel to the negative $X$-axis. This can be done by applying the magnetic field along

Vedclass Test Series

Exam Paper Generator

Online Exam Module