Study Notes for Engineering Physics I - Prof. Sanjiv Badhe

Overview of Engineering Physics I

Module 1: Quantum Physics

Session 1: De Broglie Hypothesis of Matter Waves

• Origin of Quantum Physics:   - Concept introduced by Max Planck to explain black body radiation.   - A black body absorbs nearly all incident radiation and emits radiation that contains all wavelengths.   - The temperature increases and radiation is emitted with a peak wavelength defined by Wien's Law.   - Max Planck’s law of radiation states:   $E = h u$ where:
  low[ h =\text{Planck's constant}, \nu = \text{frequency} ]

De Broglie Hypothesis:

• Every moving particle exhibits wave properties.

• Wavelength is given by:   $\lambda = \frac{h}{mv}$   where:   - $h$ = Planck's constant   - $m$ = mass   - $v$ = velocity

Proof of De Broglie Relation:

1. For photons:    - Energy: $E = h u$    - Momentum: $p = \frac{E}{c}$

2. For material particles:    - Using Einstein's Energy-Mass relation:    $E = mc^2$

3. Combining gives:    - $\frac{p}{h} = rac{\nu}{c}$    - By assuming that the relation holds for all matter particles, get:    $\lambda = \frac{h}{mv}$

Justification Using Bohr’s Postulates:

• In an atom, angular momentum is quantized:   L = n \h

• De Broglie wavelength helps establish quantized orbits.

Experimental Verification of De Broglie Hypothesis:

• Davisson and Germer Experiment:   - Setup with an electron gun, accelerating anode, and Nickel target.   - Confirmed diffraction patterns indicating wave properties of electrons.

Properties of Matter Waves:

• Matter waves are linked to particles and not electromagnetic waves.

• Wavelength inversely relates to mass and velocity:   - $\lambda \propto \frac{1}{mv}$

• Matter waves propagate in a vacuum (distinct from mechanical waves).

Numerical Problems on De Broglie Hypothesis:

• Example Problem (Electron Beam Acceleration):   - Find the wavelength of an electron beam accelerated with a potential difference of 200V.

• Example Problem (Neutron Wavelength):   - Calculate the wavelength for a neutron moving with 0.025 eV of energy.

Module 2: Crystallography

Session 1: Unit Cell, Space Lattice, and Crystal Structure

• Definitions:   - Unit Cell: Smallest repeating unit in a crystal.   - Space Lattice: 3D arrangement of points in space representing atoms or molecules.

Crystal Types:

1. Crystalline Solids: Regular arrangement of atoms, examples: Metals, Ceramics.

2. Amorphous Solids: Irregular structure, examples: Glass, Plastics.

Importance of Studying Crystal Physics:

• Relate microscopic properties to macroscopic behaviors of materials in engineering applications.

Electronic Properties of Materials

Semiconductor Physics:

• Energy Bands: Formation of energy bands in solids;   - Conductors, Semiconductors, and Insulators based on band theory.

Hall Effect:

• Description: Voltage induced across a conductor when it carries a current and is placed in a magnetic field.   - Current is deflected, which correlates to charge carriers' density.

Superconductors and Supercapacitors

Superconductors:

• Materials that exhibit zero electrical resistance below a critical temperature (Tc).

- Meissner Effect: Expulsion of magnetic fields in the superconducting state.

Supercapacitors:

• Capacitors with incredibly high capacitance values providing rapid charging/discharging ability.

• Applications: Energy storage, portable electronic devices, sensor applications, etc.

Conclusion:

• Understanding these properties and phenomena in materials is essential for engineering applications ranging from electronic devices to advanced materials technology.