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

Characteristics of electrical conduction in Metals

The general characteristics of electrical conduction in metals are summarized as follows:

1) The electrical current density in the steady state is proportional to electric field strength
     (Ohm's law).

2)  For pure specimens, the electric conductivity (σ) and the thermal conductivity (σ') vary with temperature as follows:

      σ∝T⁻¹ and σ' =const (for T > θD); θD is characteristic Debye temperature.

       so that  σ' / σT is independent of temperature (Weidmann-Franz law)

For T < θD;

      σ∝T⁻⁵ and σ' = T⁻² where 'θD' is characteristic Debye Temperature. 

      The relation  ρT⁵ is known as Bloch-Gruneisen T⁵ law.

 3) For metals that exhibit the phenomenon of superconductivity, their resistivity disappears at temperature above 0Kand below critical temperature for superconducting phase transition (critical temp=4.15K) for mercury.

4) For metals containing small amounts of impurities, the electrical resistivity(ρ) may be written as 
                                                          ρ = ρ₀ + ρ(T)
where 'ρ₀' is a constant that increases with increasing impurity content and ρ(T) is temperature dependent part of resistivity. This is known as Mattheissen's rule.

5) For most metals, the electrical resistivity decreases with increasing pressure.

6) The resistivity of alloys that exhibit order-disorder transitions shows pronounced minima corresponding to ordered phases.