Question

Derive the term magnetic dipole moment of a circular loop .write the expression for the magnetic moment when an electron revolves at a speed V' around an Orbit radius R' in hydrogen atom.​

Answer 1

For a revolving electron which carries a charge e(equal to electronic charge) , spinning around the nucleus with a radius equal to bohr radius a0, the current flowing is equal to [math]\dfrac{e}{T}=\dfrac{ev}{2\pi r},[/math]where v is the velocity of the electron.

Hence, magnetic moment= Current*Area=[math]\dfrac{ev}{2\pi r}(\pi r^2)=\dfrac{evr}{2}[/math].

Now, for calculating v, Centripetal force= Electrostatic force.

Hence,[math]\dfrac{mv^2}{r}=\dfrac{KZe^2}{r^2}.[/math]

Also, one has the orbital momentum quantization: [math]mvr=\dfrac{nh}{2\pi}[/math].

Hence, finally substitute r and v in terms of n and other known constants.

Answer 2

yep it's right

gud answer