Notes on Quantum Chemistry and Waves

  • Elementary Particles:

    • Elementary Fermions:
    • Quarks: Build protons/neutrons (hadrons).
    • Leptons: Do not form larger structures (e.g., electrons).
    • Elementary Bosons:
    • Carriers of fundamental forces (e.g., photons).

  • Properties of Waves:

    • Waves: Energy transmission in different forms (sound, light, water).
    • Amplitude:
    • Vertical distance (e.g., volume for sound, intensity for light).
    • Wavelength (6):
    • Distance between two peaks/troughs.
    • Frequency (v):
    • Wavelengths per unit time (Hertz, Hz).

  • Interference of Waves:

    • Constructive: Peaks align, increasing size.
    • Destructive: Peak aligns with trough, decreasing size.

  • Electromagnetic Waves:

    • Produced by photon interactions.
    • Includes radio waves, microwaves, infrared, visible light, ultraviolet, X-rays, and gamma rays, categorized by wavelength/frequency.

  • Quantum Theory:

    • Energy is quantized (6 = h).
    • Photoelectric effect shows frequency relevance, not just intensity.
    • Threshold frequency required to extract electrons from metals.
    • Higher frequency = higher energy electrons, not quantity.

  • Bohr’s Model:

    • Electrons transition between energy levels leading to light emission (Balmer series for hydrogen).
    • Energy of an electron is defined:
    • En = -Rh (1/n^2) where Rh = 2.18 x 10^-18 J.

  • Quantum Numbers:

    • Principal quantum number (n): Energy level.
    • Angular momentum quantum number (l): Subshell shape.
    • Magnetic quantum number (m_l): Orbital orientation.
    • Spin quantum number (m_s): Electron spin direction.

  • Magnetic Properties:

    • Paramagnetic: Unpaired spins (attracted to magnetic fields).
    • Diamagnetic: No unpaired spins (slight repulsion).

  • Examples of Quantum Numbers:

    • Sodium: n=3, l=0, ml=0, ms=+1/2 (paramagnetic).
    • Oxygen: n=2, l=1, ml=-1, ms=-1/2 (paramagnetic).
    • Vanadium: n=3, l=2, ml=0, ms=+1/2 (paramagnetic).