Quantum Mechanics Unit - I IB Tech PDF

Quantum Mechanics Unit - I I B Tech I Semester Dr. K Umadevi Applied Physics  Quantum Mechanics Introduction Black body radiation, Planck’s law, Photoelectric effect- Einstein's Photoelectric equation, Wave-Particle dualit...

Quantum Mechanics Unit - I I B Tech I Semester Dr. K Umadevi Applied Physics  Quantum Mechanics Introduction Black body radiation, Planck’s law, Photoelectric effect- Einstein's Photoelectric equation, Wave-Particle duality: de Broglie hypothesis, Davisson and Germer experiment, Heisenberg’s uncertainty principle, Born’s interpretation of the wave function, Schrodinger’s time independent wave equation, Particle in one dimensional infinite potential box. Solids: Classification of solids into metals, semiconductors, and insulators  Classical Free Electron Theory A Metal is imagined as the structure of 3-dimensional array of positive ions in which there are freely moving valence electrons confined to the body of the material. The valence electron of atoms are free to move about whole volume of metals like the molecules of a perfect gas in a container. The free electrons obey the laws of the classical kinetic theory of gasses. These free electrons move in random direction and collide with either positive ions fixed to the lattice or other electrons. All the collisions are elastic i.e. there is no loss of energy. The free electrons move in a completely uniform potential field due to positive ions fixed in the lattice. When an electric field is applied to the metal, the free electrons are accelerated in the opposite to the direction of applied electric field.  Crises in physics that demanded Quantum Mechanics ❑ Classical mechanics was introduced by Sir Issac Newton, which explains motion of macroscopic objects (large enough to be visible with naked eye). ❑ In classical mechanics, we can accurately measure mass, position, velocity, and Acceleration of a particle. ❑ However, classical mechanics failed to explain the motion of micro particles such as electrons, protons etc. ❑ Examples for the failure of Classical Mechanics are (i) Black Body radiation (ii) Specific Heat of solids at low temperature (iii) Theory of atomic structure (iv) Photo – electric effect and (v) Compton effect. ❑ To explain the failures of classical mechanics, quantum theory was developed. ❑ Quantum mechanics was introduced by Max Planck, which is indispensable in understanding the mechanics of particles in the atomic and sub-atomic scale.  Black body Radiation Perfect black body: An idealized physical body that absorbs all incident electromagnetic radiation, regardless of frequency or angle of incidence. It will not reflect or transmit a radiation at low temperatures. The same black body emits different wavelengths of radiation at constant high temperatures. ❑ Ideally there is no perfectly black body that exists. ❑ But let me introduce you to something that is very close to the black body. Vantablack: Darkest ever known substance coated on an aluminum foil. It is a substance made of vertically aligned carbon nanotubes, absorbing up to 99.965% radiation incident on it. From long to short wavelength, the EM spectrum includes radio waves, microwaves, infrared, visible light, ultraviolet, x-rays and gamma rays  Black body Black Body: In practice, a perfect black body is not available. The body showing close approximation to a perfect black body can be constructed. A hollow copper spherical shell is coated with lamp black on its inner surface. In this, a fine hole is made and a pointed projection is provided just in front of the hole (Fig. 4.1(a)). when the heat radiations enter into this spherical shell through the hole, the heat radiations suffer multiple reflections and they are completely absorbed. Now, this body acts as an absorber.  when this body is placed in a constant temperature bath at high temperature, the heat radiations comes out from the hole (Fig. 4.1(b)). Now, this hole acts as a radiator not the walls of the body. Blackbody radiation: The heat radiation emitted from a blackbody is known as blackbody radiation. The maximum energy of radiation emitted at a wavelength depends only on the temperature of a blackbody and it does not depend on the nature of the material.  Black Body Radiation Spectrum Distribution of energy in blackbody radiation: Lummer and Pringsheim in 1809 The curve in the figure shows the variation of intensity of radiation with wavelength for different temperature of the blackbody (T1 < T2 < T3