## Tuesday, November 26, 2019

### Electric Current in Atoms - Bohr Magneton ; magnetic moment of electron in orbit

The revolution of electron in its orbit around nucleus resembles a magnetic dipole and the magnetic moment due to this orbital motion of electron is

𝜇ₑ₁ = - (e/2m) x angular momentum

angular momentum = mr²w

The minus sign indicates that dipole moment points in direction opposite to vector representing angular momentum.

The ratio of magnetic dipole moment of the electron due to its orbital motion and angular momentum of orbital motion is called "orbital gyro magnetic ratio" represented by '𝛾'.

𝛾 = (magnetic moment/angular momentum) = e/2m

The strength of magnetic dipole is given by

𝜇ₑ₁ = -𝜇B.l;

𝜇B - Bohr Magneton = (eh/4πm) = 9.27 x 10⁻²⁴ Amp.m²

Therefore, '𝜇B'  represents magnetic moment of an elementary permanent magnetic dipole.

As we know that for a 'l' value there exists a quantum number 'ml' such that it takes +l to -l values hence for a d-electron for eg:

corresponding possible magnetic moment along direction of field are 2𝜇B, 𝜇B, 0, -𝜇B, -2𝜇B

Therefore  𝜇ₑ₁ = -𝜇B.ml