Quantum mechanics

• Nature of Light:

  • Light is an electromagnetic wave
  • Visible light is a small part of the EM spectrum
  • EM waves differ from sound waves as no material motion is involved, only energy
  • EM wave arises from oscillations of electric (E) and magnetic (B) fields
  • EM wave is a transverse wave
• Diffraction:

  • Waves can bend around obstacles
  • Happens with all waves
  • When a wave hits an obstacle or an aperture/opening close to its wavelength, it will bend
• Diffraction Patterns:

  • Due to interference between waves
  • Interference of light from a two-slit diffraction experiment creates fringes on the screen
  • Waves will cancel out with specific path differences, leading to destructive interference
• Single Slit Diffraction:

  • Each point on the wavefront acts as a source of spherical waves
  • If the size of the slit is small, there is significant fanning of light
• Resolution:

  • Ability to determine if light comes from one or two sources
  • Rayleigh Criterion: Two point sources are just resolved if the maximum of one diffraction pattern falls in the 1st minimum of the next pattern
• Resolution Inside the Eye:

  • Angle of resolution inside the eye is sensitive to wavelength
  • Minimum diameter of the pupil determines the resolution limit of the eye
• Aperture Size and Resolution:

  • Larger aperture size narrows the diffraction pattern
  • Sharper pattern makes it easier to resolve sources
  • Doubling the aperture size doubles the resolving distance
• Light absorption in molecules:

  • Biological molecules can convert electromagnetic wave energy into chemical energy
  • Examples include pigments involved in vision and chlorophyll
  • Most chemical reactions involve energies in the range of 1-4 eV carried by photons in the UV & visible spectrum
  • Photons in this range initiate chemical reactions by redistributing electrons involved in the bonding of molecules
• Review of the nature of light:

  • An electromagnetic wave is produced when an electrical charge is accelerated
  • Light behaves as both a wave and a particle
  • Photons are massless particles that travel in a vacuum at the speed of light
  • Energy of a photon is given by E = hf, where h is Planck's constant
  • Particles of light are called photons and obey the laws of quantum mechanics
• Photoelectric effect:

  • Light carries energy that can cause electrons to be ejected from certain materials
  • Kinetic energy of ejected electrons depends on the frequency of light, not its intensity
  • The kinetic energy of ejected electrons is equal to the energy of the incident photon minus the work function of the metal surface
• Wave-particle duality:

  • DeBroglie postulated that moving particles could have a wavelength
  • Particles exhibit wave-like properties, explaining phenomena like diffraction
  • Probability density waves represent the chance of finding particles in a specific location
• Some molecules absorb light, causing the photon to disappear and the molecule to be left at a higher energy state
• Describing electrons in an atom is done through atomic orbitals, such as S orbitals and P orbitals
• Two isolated s atomic orbitals can overlap to form the sigma orbital
• Two isolated p atomic orbitals can overlap sideways to form the pi orbital
• The wavefunction of an electron behaves like a standing wave on a string
• Actual probability of finding an electron within a region is calculated using probability density and distance (Δ𝑥)
• Energy levels of 𝝅-electrons in a linear molecule are discrete and not continuous
• Energy levels are determined by the wavelength of the standing wave and the deBroglie equation
• 𝝅 electrons occupy the lowest energy levels first and follow the Pauli Exclusion Principle
• No two electrons may occupy the same quantum state, which includes energy level and spin number
• Absorbing a photon of exact energy allows electrons to reach excited states in molecules
• Linear Molecules: π Electrons are the only electrons available to share across the molecule and are the ones that will be redistributed
• Rules for electron occupancy in linear molecules: π electrons will occupy the lowest energy levels first, and they must obey the Pauli Exclusion Principle
• Linear Molecules: Treat π-electrons as a particle-wave, where the wave function relates to the probability of finding a π-electron within the molecule
• 𝝅-electron transitions involve changes in energy levels by absorbing or emitting photons, matching the energy required for the transition
• An electronic energy level specifies the energy of a particular electron, with the ground state being when all electrons are in their lowest possible levels
• When electrons transition to higher energy levels, the molecule is in an excited state
• Photon absorption changes retinal from cis- to trans- configuration, crucial for vision in humans
• Rhodopsin, a protein in rod cells, is involved in vision and contains cis-retinal