Quantum Numbers in Chemistry

Study Notes

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).

Description

Learn about the three types of quantum numbers: principal, azimuthal, and magnetic quantum numbers. Understand their definitions, values, and roles in determining electron energy levels and orbital shapes.