Physics of Atoms and Electromagnetic Radiation

Structure of an Atom

• Nucleus: Small dense core of an atom.
  • Contains protons (+1 charge) and neutrons (no charge).
• Electron Cloud: The rest of the atom is mostly empty space filled with electrons (-1 charge).
• Nuclear Charge: Balanced by electrons moving around the nucleus.

Wavelength and Electromagnetic Radiation

• Wavelength: Distance between two peaks or troughs in a wave.
• Electromagnetic Radiation: Radiant energy behaving like a wave; travels at the speed of light.
• Frequency (v): Number of cycles per second passing a given point in space.
  • Long wavelength corresponds to short frequency.
  • Short wavelength corresponds to long frequency.
• Inversely related: c = u imes ext{Wavelength}
  • c = 2.9979 imes 10^8 ext{ m/s} (Speed of light)
  • ext{Wavelength (meters)} = rac{780 ext{ nm}}{10^9} .

Dual Nature of Light

• Light can be viewed both as a wave and as photons (packets of energy).
• Energy of Photon: Related to wavelength; emitted light corresponds to energy changes in atoms.
  • Emission Process:
  1. Atom starts in ground state (lowest energy, stable).
  2. Receives energy, becomes excited (higher energy state).
  3. Releases photons when transitioning back to ground state.
• Quantized Energy Levels: Atoms possess specific quantized energy levels resembling a staircase. Example: Hydrogen has four distinct excited states.

Quantum Theory

• Max Planck: Energy can be gained/lost in multiples of hv (where h = Planck's constant).
• Quantum Mechanics: Changes in energy are quantized, occurring in discrete units of size h .
• Energy Formula: riangle E = hv .
• Photoelectric Effect: When light strikes a metal, electrons are emitted if energy exceeds the threshold frequency ( v_0 ).
  • Formula for Kinetic Energy of emitted electrons:
    KE{electron} = E{photon} - ext{energy needed} .

Bohr Model of the Atom

• Energy Levels: Electrons occupy specific energy levels and move in circular orbits.
• Quantized Energy: Each level has a negative energy value relative to an electron completely free from the nucleus.
• Formulas: Energy levels in hydrogen: E = -rac{2.178 imes 10^{-18}}{n^2} , where n = integer (1, 2, …).
  • Electrons can only exist in defined orbits.

Wave Mechanics and Electron Behavior

• Electron Wave Function: Describes the probability of finding an electron in a given space.
• Uncertainty Principle (Heisenberg): Cannot precisely know both position and momentum of an electron simultaneously.
  • Represents the probability distribution of the electron's location.

Orbitals

• Describes regions of space where electrons can be found.
• Shape and Types:
  • s Orbitals: Spherical, one area (e.g., 1s).
  • p Orbitals: Peanut shape, two areas (e.g., 2p).
  • d Orbitals: Clover shape, four areas (e.g., 3d).
• Electron Capacity: Each orbital can hold a maximum of two electrons (Pauli Exclusion Principle).
• Filling Order: Electrons fill the lowest available energy levels first.

Atomic Size and Ionization

• Ionization Energy: Energy required to remove an electron from an atom.
  • Ionization energy increases as atoms become closer to having a filled valence shell (noble gas configuration).
• Atomic Size Trends:
  • Atomic size generally decreases across a period (increased nuclear charge) and increases down a group (more electron shells).

Conclusion

• The atomic model continues to evolve, integrating principles from quantum mechanics while seeking to explain the behavior of electrons and their interactions dynamically. Understanding these concepts is crucial for mastering atomic structure and behavior in chemistry.