Quantum Numbers in Chemistry

Quantum Numbers

• Principal Quantum Number (n):
  • Denotes the energy level of an electron
  • Takes integer values (1, 2, 3, ...)
  • Determines the average distance of an electron from the nucleus
• Azimuthal Quantum Number (l):
  • Denotes the orbital shape of an electron
  • Takes integer values (0 to n-1)
  • Determines the orbital angular momentum
• Magnetic Quantum Number (m):
  • Denotes the orientation of an orbital in a magnetic field
  • Takes integer values (-l to l)
  • Determines the number of orbitals in a subshell
• Spin Quantum Number (s):
  • Denotes the intrinsic angular momentum of an electron
  • Takes two values (+1/2 and -1/2)
  • Determines the spin of an electron

Atomic Models

• Rutherford's Atomic Model:
  • Nucleus at the center, electrons orbiting around it
  • Electrons have negative charge, nucleus has positive charge
  • Failed to explain energy levels and stability of atoms
• Bohr's Atomic Model:
  • Modified Rutherford's model by introducing energy levels
  • Electrons jump from one energy level to another by absorbing or emitting energy
  • Explained spectral lines and energy levels of atoms
• Quantum Mechanical Model:
  • Replaced Bohr's model with probability distributions of electrons
  • Introduced wave-particle duality of electrons
  • Explained all the limitations of Bohr's model

Discovery of Subatomic Particles

• J.J. Thomson's Discovery of Electron:
  • Discovered electron in 1897 using cathode ray tube
  • Determined the charge-to-mass ratio of electron
• Rutherford's Discovery of Proton:
  • Discovered proton in 1919 using alpha particle scattering
  • Determined the positive charge and mass of proton
• Chadwick's Discovery of Neutron:
  • Discovered neutron in 1932 using nuclear reactions
  • Determined the no charge and mass of neutron
• Dalton's Atomic Theory:
  • Proposed that matter consists of indivisible atoms
  • Proposed the law of definite proportions and multiple proportions

Electromagnetic Radiation

• Properties of Electromagnetic Radiation:
  • Transverse wave
  • Electric and magnetic fields perpendicular to each other
  • Velocity is constant in vacuum (c = 3 x 10^8 m/s)
  • Wavelength (λ) and frequency (ν) are related by c = λν
• Wave-Particle Duality:
  • Exhibits both wave-like and particle-like properties
  • Wave-like: diffraction, interference, superposition
  • Particle-like: quantization of energy, photoelectric effect

Quantum Numbers

• Principal Quantum Number (n) determines the energy level of an electron and the average distance of an electron from the nucleus, taking integer values (1, 2, 3,...).
• Azimuthal Quantum Number (l) determines the orbital shape of an electron and orbital angular momentum, taking integer values (0 to n-1).
• Magnetic Quantum Number (m) determines the orientation of an orbital in a magnetic field and the number of orbitals in a subshell, taking integer values (-l to l).
• Spin Quantum Number (s) determines the intrinsic angular momentum of an electron, taking two values (+1/2 and -1/2).

Atomic Models

• Rutherford's Atomic Model: nucleus at the center, electrons orbiting around it, with electrons having negative charge and nucleus having positive charge, but failed to explain energy levels and stability of atoms.
• Bohr's Atomic Model: modified Rutherford's model by introducing energy levels, where electrons jump from one energy level to another by absorbing or emitting energy, explaining spectral lines and energy levels of atoms.
• Quantum Mechanical Model: replaced Bohr's model with probability distributions of electrons, introducing wave-particle duality of electrons, and explained all the limitations of Bohr's model.

Discovery of Subatomic Particles

• J.J. Thomson discovered electron in 1897 using cathode ray tube, determining the charge-to-mass ratio of electron.
• Rutherford discovered proton in 1919 using alpha particle scattering, determining the positive charge and mass of proton.
• Chadwick discovered neutron in 1932 using nuclear reactions, determining the no charge and mass of neutron.
• Dalton proposed atomic theory, stating that matter consists of indivisible atoms, and proposed the law of definite proportions and multiple proportions.

Electromagnetic Radiation

• Electromagnetic radiation has properties of a transverse wave, with electric and magnetic fields perpendicular to each other, and a constant velocity in vacuum (c = 3 x 10^8 m/s).
• Electromagnetic radiation exhibits wave-particle duality, with wave-like properties (diffraction, interference, superposition) and particle-like properties (quantization of energy, photoelectric effect).