The Davisson-Germer Experiment

The experiment gave the evidence of wave nature possession by materialistic particle(electron) for the first time.

The arrangement of equipment used for the experiment is as follows

                      Procedure:

An electron gun is used in order to produce electrons. The electrons so produced are accelerated by applying a high potential towards the target crystal, in this case the target crystal is nicker. The accelerated electron beam is made into fine beam by passing it through a Collimator ‘c’.

The crystal is mounted on an arrangement which could be rotated in different directions perpendicular to the plane of diagram.

The electrons are scattered in all directions by atomic planes of crystal.

The intensity of electron beam ( no. Of electrons) scattered in a particular direction is measured by electron collector which can be rotated about the same axis as target crystal.

The collector is connected to a sensitive Galvanometer whose deflection is proportional to intensity of electron beam entering collector . The electron collector is also called Faraday cylinder.

A retarding potential is applied to Faraday cylinder such that only fast electrons can reach it and secondary electrons emitted from crystals are stopped.

A graph is then plotted between galvanometer current against angle ‘θ' between incident beam and diffracted beam i.e, beam entering Faraday cylinder.



In the investigation , the electron beam accelerated by 54V and at an angle of 50 between incident and diffracted beam , a sharp maximum has occurred in electron distribution.

The incident beam and diffracted beam in this experiment make an angle of 65⁰   with Braggs plane. 

For a 54 V electron , the de-broglie wavelength associated with the electron is given by

ƛ = 12.25/√V = 12.25/√54 A⁰ = 1.66 A⁰ 

Now from Bragg’s equation for maxima in diffraction pattern for same energy electrons

2d sinθ' = nƛ; 2*0.91*10^-10*sin 65⁰ = 1*ƛ;

ƛ = 1.65 A⁰ 

Thus, both theoretical and experimental values are in excellent agreement.

Thus Davission - Germer experiment provides a direct verification of de-broglie hypothesis of wave nature of moving particles.

PIN Diode - General Description

It is a junction photo diode. 

Basic principle :- The diode is operated under reverse biased condition. Under photo excitation , photons are absorbed mainly in depletion region and also in neutral region , particularly on top where light is incident. the absorbed photons create e-h pairs

They give rise to photo current , the magnitude of which depends on quantum efficiency.

so photo excitation is therefore detected as an increase in reverse biased current of a junction photo diode.

Large depletion layer may increase no.of e-h pairs generated but it consequently increases response time of diode degrading its high speed performance.

Pin diodes have no internal gain but can have very large band widths.

Since dark current in a reverse biased junction is very small , pin diode is more sensitive device than a photo conductor.

Difference between Impedance and Reactance

For all the circuits lumped elements in which time varying voltages / current exists , we find a relation in which the voltage is proportional to Current . The proportional quantity is in general a complex number and this is called Impedance.

It is a function of frequency of ‘w’ strictly speaking impedance is sum of its real and imaginary parts.

Z= R+ IX

Impedance is equivalent to a Resistance in series with pure imaginary Impedance - called a Reactance.

The voltage drop across the resistance is in phase with the current , while the voltage drop across the purely Reactive part is out of phase with the current.

The average energy loss in an impedance Z= R + iX depends only on real part of ‘Z’ and not on complex part.

There is no energy loss in Reactive part.

GP THOMSON EFFECT - Experimental Verification of Wave nature of Matter

G P  Thomson has performed experiments with electrons accelerated from 10000 to 50000 volts.

The high energy beam of electrons is produced by a cathode ‘C’.

The experimental arrangement is as shown below:

The electron beam is excited with potential upto a maximum of 50,000 volts. A fine beam is obtained by passing it through slit or diaphragm ‘S’.

The accelerating fine beam of electrons now falls on thin gold or Aluminum film (order of 10^-6 cm thickness).

The photograph of beam from foil is recorded on photographic plate ‘P’.

After developing the plate, a symmetric pattern consisting of concentric rings about a central spot is obtained. This pattern resembles that of X- rays.

To know that this pattern is due to electrons or due to x-rays generated by electrons in their passage through foil, cathode rays in discharge tube are deflected by magnetic field.

It was observed that beam shifts correspondingly showing there by that pattern is produced by electrons and not by x-rays.  (i.e X – ray pattern is not affected by electric and magnetic fields).

As diffraction pattern can only be produced by waves and not by particles, so Thomson concluded that electrons behave like wave.

Thus, Thomson experiment clearly demonstrated the existence of matter waves.

BCS (Bardeen - Cooper - Schieffer) THEORY

The microscopic theory put forward by Bardeen, Cooper and Schreiffer (BCS), in 1957 provides the better quantum explanation of  superconductivity and explains well all the properties exhibited by superconductors.

The basis of formulation of BCS theory are two experimental conclusions namely the isotope effect and variation of specific heat of superconductors.

For isotope effect Tc M^1/2 = constant, one can infer that transition resulting in superconducting state must involve dynamics of ion motions, lattice vibrations and Phonons.

Further we note that Tc attains a value zero when 'M' approaches infinity. This all suggests that the non zero transition temperature is a consequence of finite mass of ions which can contribute Phonons by their vibrations.

Bardeen pointed out that an electron moving through a crystal lattice has a self energy accompanied by virtual Phonons. This means that an electron moving through crystal lattice distorts the lattice and lattice in turn acts on  electron by virtue of electrostatic forces between them. The oscillatory distortion of lattice is quantized in terms of Phonons and so one can interpret the interaction between lattice and electron as constant emission and re-absorption of Phonon by latter. These are called virtual Phonons.

BCS showed that basic interaction responsible for responsible for superconductivity appears to be that of a pair of electrons by means of interchange of virtual Phonons.

Suppose an electron approaches a positive ion core . It suffers attractive Coulomb interaction. Due to this attraction ion core is set in motion and consequently distorts the lattice. 

Smaller the mass of positive ion core, the greater will be the distortion. Suppose towards that site another electron comes and sees this distorted lattice. Then the interaction between the two, the electron and distorted lattice occurs which in its effect lowers the energy of second electron. 

Thus, we interpret that the two electrons interact via the lattice distortion or the Phonon field resulting in lowering of energy for electrons.

The lowering of electron energy implies that force between two electrons is attractive. This type of interaction is called electron-lattice-electron interaction. This interaction is strongest when two electrons have equal and opposite momenta and spins.

Since the oscillator distortion of Lattice is quantized in terms of Phonons, the above interaction can be interpreted as electron-electron interaction through Phonon as mediator.

Let an electron of wave vector K1 emits a virtual phonon 'q' which is absorbed by an electron with wave vector K2. K1 is thus scattered as K1-q and K2+q.

The nature of resulting electron-electron interaction depends on relative magnitudes of electronic energy and phonon energy. If the phonon energy exceeds electronic energy, the interaction is attractive.

When such interaction occurs by phonon exchange by dominating usual repulsive interaction, two such electrons from a pair called as Cooper pair.

The energy of pair of electrons in bound state is less than energy pair in free state. The difference in energy of two states is binding energy of cooper pair.

The energy difference between free state of electron and paired state appears as energy gap at Fermi surface. The normal electron states are above the energy gap and superconducting  electron states are below the energy gap at Fermi surface.