PRINCIPLE OF ELECTRON SPIN RESONANCE (ESR)

Electron Spin Resonance (ESR) is a branch of absorption spectra in which radiation having frequency in microwave region is absorbed by paramagnetic substances to induce transitions between magnetic energy levels of electrons with unpaired spins.

ESR also called Electronic Paramagnetic Resonance is a spectroscopic technique confined to study of those species having one or more unpaired electrons.

Phenomenon of ESR was invented by Zaveiskii in 1904.


PRINCIPLE OF ESR

When we consider an unpaired electron it is associated with spin. When a magnetic field is applied, the magnetic moment of electron interacts with field and results in splitting of otherwise degenerate field. Now the energy difference between the levels falls in microwave region.So when radiation in microwave range equal to this energy difference is made to incident on substance, transitions occur between these levels absorbing quanta of energy leading to a absorption peak.

Only spin moment contributes towards the magnetic behaviour of electrons.

Consider that system has only spin magnetic moment

μ= -gμBS ....................................(1)

'μ' & 's' are in opposite directions.

For an electron of spin S=1/2, the spin angular momentum quantum number will have values
ms = ±1/2 ..................................(2)

In absence of magnetic field, the two values of 'ms' i.e. +1/2 and -1/2 will give rise to a doubly degenerate spin energy state.

When magnetic field is applied this degeneracy is removed and thus leads to two non degenerate energy levels.

Now the interaction energy is given by

Polar Dielectric in uniform electric field

There are permanent dipoles present in polar dielectric which are randomly aligned in such a way that there is permanent dipole moment Pp. [see fig a]

 
When a dipole is present in an uniform electric field the dipole tries to align itself in the direction of electric field.

Because of this all dipoles in a polar dielectric are partially aligned in the direction of field. This partial alignment is responsible for the induced dipole moment Pi.[see fig b].                 
Therefore, the electric dipole moment is increasing.   

P =  Pp + Pi

The electric dipole moment of a polar dielectric increases
a) by increasing the applied E.
b) by decreasing the temperature
 

Dielectrics - Polar, Non Polar, uses

A dielectric is a non conducting substance introduced between the plates of a capacitor.

What is Non Polar Dielectric?

This is a substance in which the net electric dipole moment is zero because of its symmetrical structure. In this the center of gravity of positive charges and  center of gravity of negative charges
will coincide.

What is Polar Dielectric?

Because of their non symmetrical structure these dielectrics have permanent dipole moment. In this there are permanent electric dipoles present. On this if an external electric field is applied, torque acts on these dipoles rotating them in direction of applied electric field. When an external electric field is applied on non polar dielectric this dielectric gets polarized forming induced charges on the surfaces.      

Uses of Dielectric

1. It maintains mechanical separation between the plates.

2. It decreases the field as well as potential but increases the capacity

3.  Increases capacitance between metal plates
When a non polar dielectric is introduced between the plates it is leading to the displacement of negative charges in the dielectric. Because of the displacement of negative charges, the center of gravity of negative charges is not coinciding the center of gravity of positive charges, thus forming dipoles. This phenomenon of formation of electric dipoles when an external electric field is applied on a non-polar dielectric is known as Polarisation. 

Therefore, induced charges are appearing on the surfaces of dielectric forming their own electric field  Eᵢ. This Eᵢ opposes original electric field Eₒ, thus net electric field E is decreasing.

E=Eₒ-Eᵢ

Therefore, potential between the plates is also decreasing resulting in increase in capacitance.

4. Used for withstanding high potentials
 Any dielectric can withstand a maximum electric field before becoming a partial conductor. This maximum electric field, a dielectric can withstand before reaching breakdown condition is known as dielectric strength of dielectric.
Therefore, heavy capacitors use dielectrics using highest dielectric strengths to withstand large potentials. 
 

Quantities from Kinetic Theory of Gases

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  ρ∝T⁵ 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 + ρᴘ(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.