Question

Give the expression for gyromagnetic ratio of electrons and explain the terms

Answer 1

$$\begin{gathered} Dearstudent \\ gyromagneticratio=\frac{magneticinduction}{angualrmomentum} \\ =\frac{IA}{mvr} \\ =\frac{{\displaystyle \frac{q}{t}}\pi R^2}{m_{e}vR}----\left(1\right) \\ \frac{m_e{v}^2}{R}=\frac{k{e}^2}{R^2} \\ v=\sqrt{\frac{k{e}^2}{m_{e}R}} \\ t=\frac{2\pi R}{v}=\frac{2\pi R}{\sqrt{\frac{k{e}^2}{m_{e}R}}} \\ from1 \\ gyromagneticratio=\frac{{\displaystyle \frac{q}{t}\pi R^2}}{m_{e}vR}=\frac{{\displaystyle q\pi R^2}}{t{m}_{e}vR}=\frac{{\displaystyle q\pi R^2}}{\frac{2\pi R}{\sqrt{\frac{k{e}^2}{m_{e}R}}}{m}_{e}vR}=\frac{{\displaystyle q\sqrt{k{e}^2}}}{2m_{e}v\sqrt{m_{e}R}} \\ =\frac{{\displaystyle q\sqrt{k{e}^2}}}{2m_e\sqrt{\frac{k{e}^2}{m_{e}R}}\sqrt{m_{e}R}} \\ =\frac{{\displaystyle q\sqrt{k{e}^2}\sqrt{m_{e}R}}}{2m_e\sqrt{k{e}^2}\sqrt{m_{e}R}}=\frac{{\displaystyle e}}{2m_e} \\ Bohrmagnetonisaunitusedforexpres\sin gthemagneticmomentofanelectroncausedbyeitheritsorbitalorspinangularmomentum. \\ Regrads \end{gathered}$$