.Derive an expression for the magnetic dipole moment of a revolving electron and
hence define Bohr magneton.

Dear Student
Bohr's magneton is a  physical constant which expresses the magnetic moment of electron in terms of orbital or spin angular momentum
$$\begin{gathered} let electron of mass m and charge e revolving around the nucleus \\ then \\ M=iA=\frac{e}{T}\times \pi r^2=\frac{e}{{\displaystyle \frac{2\pi r}{v}}}\times \pi r^2=\frac{ev\times \pi r^2}{2\pi r}=\frac{evr}{2}...1> \\ L(angular momentum)=mvr=nh \\ mvr=1\times h \\ v=\frac{h}{mr}...2> \\ now putting the value of v in eq 1 we get \\ M=\frac{e{\displaystyle \frac{h}{mr}}r}{2}=\frac{eh}{2m} \\ Regards \end{gathered}$$