The gyromagnetic ratio and Bohr magneton are | vedclass

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Question

(A) The gyromagnetic ratio is defined as the ratio of the magnetic dipole moment $(M)$ to the angular momentum $(L)$ of an electron orbiting in an ato

Vedclass · Accepted Answer

$\frac{e}{2m}, \frac{eh}{4\pi m}$

Vedclass · Answer

(A) The gyromagnetic ratio is defined as the ratio of the magnetic dipole moment $(M)$ to the angular momentum $(L)$ of an electron orbiting in an atom.For an electron in an orbit,the magnetic moment $M = I A = (\frac{e}{T}) (\pi r^2) = \frac{e}{2\pi r/v} (\pi r^2) = \frac{evr}{2}$.The angular momentum $L = mvr$.Thus,the gyromagnetic ratio $\gamma = \frac{M}{L} = \frac{evr/2}{mvr} = \frac{e}{2m}$.The Bohr magneton $(\mu_B)$ is the fundamental unit of magnetic moment,given by $\mu_B = \frac{eh}{4\pi m}$.Therefore,the gyromagnetic ratio and Bohr magneton are $\frac{e}{2m}$ and $\frac{eh}{4\pi m}$ respectively.

The gyromagnetic ratio and Bohr magneton are given respectively by [Given $\rightarrow e=$ charge on electron,$m=$ mass of electron,$h=$ Planck's constant].

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