Lecture on Quantum Physics and Electron Microscopy

Lecture Overview

  • Lecture № 11 Topics:
    • Quantum physics
    • Electronic microscope
    • Thermal radiation
    • Solar radiation
    • Infrared and ultraviolet diagnostics and therapy
    • Types of optical transitions
    • Luminescence
    • External and internal photoelectric effect

Photons and de Broglie Waves

  • Photons:
    • Definition: Particle-like quanta of electromagnetic radiation
    • Properties: Travel at the speed of light (c) with momentum (p) and energy (W)
    • Relationships:
    • W = h
      u
    • rac{
      u}{ rac{1}{
      u}} = rac{hc}{h
      u}
    • p = rac{h}{
      u}
  • de Broglie Hypothesis:
    • Proposed by Louis de Broglie in 1923
    • Statement: Particles of matter, such as electrons, can exhibit wave-like properties.
    • Wave wavelength for a particle with momentum (p):
    • rac{mv}{h}
  • de Broglie Wavelength:
    • Experimental confirmations since 1927 show protons, neutrons, atoms, and molecules exhibit wave-like behavior.
  • Differences from Classical Waves:
    • de Broglie waves are attributed to microparticles.
    • Do not have counterparts in classical physics.

Experimental Verification of de Broglie's Hypothesis

  • Experiments by Tartakovsky and Thomson:
    • Demonstrated diffraction patterns with light, atoms (H, H2, He), protons, and neutrons.
  • Key Equations:
    • Optical path difference determined by:
    • ext{Δ} = 2AB = 2d ext{sin} heta
    • Wulff–Bragg Condition:
    • 2d ext{sin} heta = n ext{λ}; n = 1, 2, …
  • Noteworthy Results:
    • Experiments in 1927 showed that electrons behave like waves.
  • Wavelength Calculation Example:
    • For U = 100 kV,
    • ext{λ} ext{approx} = 4.10^{-12} ext{m} = 400 ext{pm}

Electron Microscopes (EM)

Working Principle

  • Functionality:
    • EMs utilize electron beam interaction with a sample to gather structural and compositional information.
    • Components:
    • Electron gun generates electrons.
    • Two condenser lenses focus the electron beam on the specimen.
    • Accelerating voltage between tungsten filament and anode (typically 100 kV to 1000 kV).
  • Sample Preparation:
    • Specimens must be ultra-thin (20-100 nm thickness), at least 200 times thinner than those in optical microscopes.
    • Electron Interaction:
    • Electrons scatter based on differing density or refractive index within the sample.
    • Denser areas appear darker as fewer electrons reach the imaging screen; lighter areas indicate transparency.

Types of Electron Microscopes

  • Categories:
    • Transmission Electron Microscope (TEM)
    • Scanning Electron Microscope (SEM)
    • Field Emission Scanning Electron Microscopy (FESEM)
    • Reflection Electron Microscopy (REM)
    • Scanning Tunneling Microscopy (STM)

Transmission Electron Microscopy (TEM)

Overview

  • Purpose:
    • Used for imaging thin specimens such as tissue sections and molecular structures.
  • Operation Modes:
    • Imaging Mode: Obtains images of samples.
    • Diffraction Mode: Determines crystal orientation and cell structure.
  • Sample Thickness:
    • Ultra-thin sections < 100 nm, placed on a copper grid around standard size (3.05mm diameter).
  • Voltage Ranges:
    • Ordinary (50-100 kV) and high voltage (up to 3 MV).
  • Imaging Capabilities:
    • High resolution with maximum magnification
    • Can image carbon atoms (0.089 nm) and silicon atoms (0.078 nm) at magnifications > 50 million times.

Scanning Electron Microscopy (SEM)

Characteristics

  • Operation:
    • Based on secondary and backscattered electron emission.
    • Reveals surface morphology, chemical composition, and crystalline structure.
    • Utilizes lower voltage than TEM (30-40 kV).
  • Image Formation:
    • Secondary electrons contribute surface imaging with high resolution < 1 nm.
    • Backscattered electrons provide deeper insights (lower resolution) for multi-phase compositions.
  • Advantages:
    • Greater depth portrayal; provides 3D structure representation.

Infrared and Ultraviolet Radiation

Infrared Diagnostics and Therapy

  • Infrared Radiation Characteristics:
    • Wavelength: 0.8 µm - 1000 µm.
    • Body temperature (37 °C): λmax ≈ 9.5 µm.
  • Therapeutic Applications:
    • Traditional and modern infrared lamps (e.g., Solux lamps) for various treatment methodologies.

Ultraviolet Diagnostics and Therapy

  • Ranges:
    • UV Spectrum: 10 nm - 400 nm (e.g., UV-A, UV-B, UV-C)
  • Health Implications:
    • Overexposure risks like skin cancer, cataracts.
    • Therapeutic doses beneficial for vitamin D production.

Quantum Optical Phenomena

Thermal Radiation

  • Definition:
    • EM radiation from the thermal motion of particles.
  • Stefan-Boltzmann Law:
    • E = σT^4 where σ represents the Stefan–Boltzmann constant.
  • Planck’s Law of Blackbody Radiation:
    • E = hν where h is Planck's constant and ν is frequency.

Types of Optical Transitions

Quantum Transitions

  • Absorption:
    • Photon absorbed matching energy separation between quantized states.
  • Emission Types:
    • Spontaneous and stimulated emissions.
  • Stokes' Law:
    • Emission occurs at longer wavelengths than absorption.

Luminescence

Types of Luminescence

  • Forms:
    • Photoluminescence, electroluminescence, and chemiluminescence.
  • Applications:
    • Medical diagnostic tools using fluorescence analysis for tracking substances in biological tissues.

Photoelectric Effect

External Effect

  • Definition:
    • Emission of electrons from materials when excited by electromagnetic radiation.
  • Key Points:
    • Electrons emitted are called photoelectrons.
    • Occurred study by Hertz & Stoletov – emission from metals conditions.
  • Conductivity Implications:
    • Photoconductivity in semiconductors through exposure to light.

Solar Cells

Structure and Working

  • Construction:
    • Silicon photovoltaic cells with p-n junctions for light detection and power supply.
  • Production Data:
    • Typical solar cell output of 1 watt with efficiency of ~15% based on duration of exposure.