The magnetic moment (m_{orb}) of a revolving | vedclass

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

Question

(D) The orbital magnetic moment is defined as $m_{orb} = iA$,where $i = \frac{e}{T}$ is the current,$A = \pi r^2$ is the area,and $T$ is the time peri

Vedclass · Accepted Answer

$m_{orb} \propto n$

Vedclass · Answer

(D) The orbital magnetic moment is defined as $m_{orb} = iA$,where $i = \frac{e}{T}$ is the current,$A = \pi r^2$ is the area,and $T$ is the time period of the electron's revolution.Substituting $i$ and $A$,we get $m_{orb} = e \left( \frac{\pi r^2}{T} \right) \dots (1)$.According to Bohr's quantization condition for angular momentum,$mvr = \frac{nh}{2\pi} \dots (2)$.Also,the time period $T$ is related to velocity $v$ and radius $r$ by $T = \frac{2\pi r}{v}$,which implies $\frac{r}{T} = \frac{v}{2\pi}$.Substituting this into the expression for $m_{orb}$,we get $m_{orb} = e \pi r \left( \frac{r}{T} \right) = e \pi r \left( \frac{v}{2\pi} \right) = \frac{evr}{2}$.From equation $(2)$,$vr = \frac{nh}{2\pi m}$.Substituting this into the expression for $m_{orb}$,we get $m_{orb} = \frac{e}{2} \left( \frac{nh}{2\pi m} \right) = n \left( \frac{eh}{4\pi m} \right)$.Since $e, h, \pi,$ and $m$ are constants,we conclude that $m_{orb} \propto n$.

The magnetic moment $(m_{orb})$ of a revolving electron around the nucleus varies with the principal quantum number $(n)$ as

Similar Questions

Let $A_n$ be the area enclosed by the $n^{th}$ orbit in a hydrogen atom. The graph of $\ln (A_n/A_1)$ against $\ln (n)$:

The Hitomi satellite recently observed the Lyman alpha emission line ($n=2$ to $n=1$) of hydrogen-like iron ion (atomic number of iron is $26$) from the Perseus galaxy cluster. The wavelength of the line is closest to ............... $\mathring{A}$.

In a hydrogen atom,if $V_n$ and $V_p$ are the orbital velocities in the $n^{\text{th}}$ and $p^{\text{th}}$ orbits respectively,then the ratio $V_p : V_n$ is:

The Bohr model of atoms:

Vedclass Test Series

Exam Paper Generator

Online Exam Module