The gyromagnetic ratio of an electron in a hy | vedclass

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

Question

(B) The gyromagnetic ratio is defined as the ratio of the magnetic moment $\mu$ to the angular momentum $L$ of the electron.$	ext{Gyromagnetic ratio}

Vedclass · Accepted Answer

independent of which orbit it is in

Vedclass · Answer

(B) The gyromagnetic ratio is defined as the ratio of the magnetic moment $\mu$ to the angular momentum $L$ of the electron.$	ext{Gyromagnetic ratio} = \frac{\mu}{L} = \frac{iA}{mvr}$Using the Bohr model,the current $i = \frac{e}{T} = \frac{e \omega}{2 \pi}$ and the area $A = \pi r^2$.The angular momentum $L = mvr = mr(r \omega) = mr^2 \omega$.Substituting these values:$\frac{\mu}{L} = \frac{(\frac{e \omega}{2 \pi})(\pi r^2)}{mr^2 \omega} = \frac{e}{2m}$Since $e$ and $m$ are constants,the gyromagnetic ratio is independent of the orbit $n$ of the electron.

The gyromagnetic ratio of an electron in a hydrogen atom,according to the Bohr model,is

Similar Questions

The magnetic moment $(\mu)$ of an electron revolving around the nucleus varies with the principal quantum number $n$ as

$A$ sample of hydrogen-like atoms produces an emission spectrum consisting of $10$ wavelengths arising from all possible transitions. During this process,the maximum angular momentum change for an electron transitioning from a higher energy level to a lower energy level is:

State the success of the Bohr's atomic model.

The momentum of an electron revolving in the $n^{\text{th}}$ orbit is given by: (Symbols have their usual meanings)

Using Bohr's model,calculate the ratio of the magnetic fields generated due to the motion of the electrons in the $2^{nd}$ and $4^{th}$ orbits of hydrogen atom. (in $32$ : $1$)

Vedclass Test Series

Exam Paper Generator

Online Exam Module