Undergraduate
  1. General chemistry  1.1. Introduction to Chemistry  1.2. Atomic Structure  1.2.1. Subatomic particles  1.2.2. Atomic Model  1.2.3. Quantum numbers  1.2.4. Electron Configuration  1.2.5. Periodic trends  1.2.6. Isotopes and their applications  1.3. Chemical bond  1.3.1. Ionic bond  1.3.2. Covalent bonds  1.3.3. Metal Bond  1.3.4. Hybridization  1.3.5. Molecular geometry and VSEPR theory  1.3.6. Bond polarity and dipole moment  1.4. Stoichiometry  1.4.1. Mole concept  1.4.2. Empirical and molecular formula  1.4.3. Limiting reactant and excess reactant  1.4.4. Percent Yield and Purity  1.4.5. Dilution calculation  1.5. States of matter  1.5.1. Gas Laws  1.5.2. Matter and Intermolecular Forces  1.5.3. Solid and Crystal Structures  1.5.4. Phase diagram  1.5.5. Plasma and supercritical fluid  1.6. Chemical reactions  1.6.1. Types of Chemical Reactions  1.6.2. Balancing Chemical Equations  1.6.3. Thermochemical reactions  1.6.4. Reaction energy profiles  1.7. Solutions and Mixtures  1.7.1. Concentration units  1.7.2. Syndrome properties  1.7.3. Solubility and Solubility Rules  1.7.4. Henry's Law and Raoult's Law  1.7.5. Partition coefficient  1.8. Chemical equilibrium  1.8.1. Law of mass action  1.8.2. Le Chatelier's principle  1.8.3. Reaction quotient  1.8.4. To use this online calculator for Equilibrium Constant, enter Equilibrium Constant (Eq.) and hit the calculate button. Here is how the Equilibrium Constant calculation can be explained with given input values -> 0.05 = 0.05/0.  1.8.5. Acid-base balance  1.9. Acids and bases  1.9.1. Arrhenius, Brønsted–Lowry, and Lewis definitions  1.9.2. pH and pOH  1.9.3. Acid-base titration  1.9.4. Buffer Solution  1.9.5. Acid-base indicator  1.9.6. Polyprotic Acids and Bases  1.10. Electrochemistry  1.10.1. redox reactions  1.10.2. Galvanic and Electrolytic Cells  1.10.3. Nernst equation  1.10.4. Electrolysis  1.10.5. Faraday's laws of electrolysis  1.11. Thermodynamics  1.11.1. Laws of Thermodynamics  1.11.2. Enthalpy, entropy and Gibbs free energy  1.11.3. Spontaneity of reactions  1.11.4. Thermodynamic cycles (Hess's law, Carnot cycle)  1.12. Kinetics  1.12.1. Rate law and reaction order  1.12.2. Activation Energy and Catalyst  1.12.3. Collision theory  1.12.4. Reaction mechanism  1.12.5. Transition state theory
  2. Organic chemistry  2.1. Structure and relationships  2.1.1. Hybridisation in Carbon Compounds  2.1.2. Resonance and aromatization  2.1.3. Molecular orbitals  2.1.4. Inductive and mesomeric effects  2.2. Hydrocarbons  2.2.1. Hydrocarbons  2.2.2. Alkene  2.2.3. Alkynes  2.2.4. Aromatic compounds  2.2.5. Cycloalkanes and Conformation  2.3. Functional Group  2.3.1. Alcohols and phenols  2.3.2. Ethers and epoxides  2.3.3. Aldehyde and ketone  2.3.4. Carboxylic acids and derivatives  2.3.5. Amin  2.3.6. Esters and amides  2.3.7. Thiols and sulfides  2.4. Stereoscopic  2.4.1. Isomerism in Stereochemistry  2.4.2. Chirality and optical activity  2.4.3. Structural analysis  2.4.4. Diastereomers and Enantiomers  2.5.1. Substitution reactions  2.5.2. Elimination reactions  2.5.3. Addition reactions  2.5.4. Radical reactions  2.5.5. Rearrangement reactions  2.5.6. Pericyclic Reactions  2.6. Spectroscopy and structural analysis  2.6.1. Infrared Spectroscopy  2.6.2. Nuclear magnetic resonance spectroscopy  2.6.3. Mass Spectrometry  2.6.4. UV-visible spectroscopy  2.6.5. X-ray crystallography  2.7. Polymer chemistry  2.7.1. Addition and Condensation Polymers  2.7.2. Polymerization mechanism  2.7.3. Biodegradable Polymer  2.7.4. Conducting and smart polymers
  3. Inorganic chemistry  3.1. Coordination chemistry  3.1.1. Ligands and coordination compounds  3.1.2. Crystal field theory  3.1.3. Molecular Orbital Theory in Coordination Compounds  3.1.4. Jahn–Taylor distortion  3.2. Main Group Chemistry  3.2.1. Alkali and alkaline earth metals  3.2.2. Halogens and Noble Gases  3.2.3. Transition metals and their complexes  3.2.4. Lanthanides and Actinides  3.3. Solid state chemistry  3.3.1. Crystal lattices and unit cells  3.3.2. Defects in solids  3.3.3. Electrical and magnetic properties  3.3.4. Superconductivity  3.4. Bio-inorganic chemistry  3.4.1. Metal ions in biology  3.4.2. Enzymatic reactions with metals  3.4.3. Metal poisoning and detoxification  3.4.4. Metalloproteins and Metalloenzymes
  4. Physical chemistry  4.1. Quantum Chemistry  4.1.1. Wave–particle duality  4.1.2. Schrödinger Equation  4.1.3. Quantum Numbers and Orbitals  4.1.4. Atomic and molecular spectroscopy  4.2. Statistical mechanics  4.2.1. Maxwell–Boltzmann distribution  4.2.2. Partitioning functions  4.2.3. Bose–Einstein and Fermi–Dirac statistics  4.3. Chemical thermodynamics  4.3.1. Gibbs Free Energy  4.3.2. Phase transition  4.3.3. Thermodynamic efficiency  4.4. Surface chemistry  4.4.1. Absorption and Catalysis  4.4.2. Colloids and Emulsions
  5. Analytical Chemistry  5.1. Classical methods  5.1.1. Gravimetric Analysis  5.1.2. titrimeter  5.2. Instrumental methods  5.2.1. Chromatography  5.2.2. Spectroscopy  5.2.3. Electroanalytical methods  5.2.4. X-ray diffraction
  6. Industrial Chemistry  6.1. Petrochemistry  6.2. Chemical engineering principles  6.3. Green Chemistry  6.4. Pharmaceuticals and Drug Synthesis
  7. Biochemistry  7.1. Carbohydrates  7.2. Proteins and enzymes  7.3. Lipids and membranes  7.4. Nucleic acids  7.5. Metabolism and Bioenergetics  7.6. Enzyme kinetics and mechanism

Undergraduate → General chemistry → Atomic Structure ↓


Quantum numbers


Understanding the structure of atoms is fundamental in chemistry. Atoms, which are the basic units of matter, are composed of protons, neutrons, and electrons. Of these, electrons play a major role in chemical bonding and determine the chemical properties of an atom. Electrons reside in regions of space around the nucleus called orbitals. These orbitals can be described using quantum numbers.

Quantum numbers are sets of numerical values that provide solutions to the Schrödinger equation for the hydrogen atom. They describe various properties of orbitals and the properties of electrons within these orbitals. There are four quantum numbers, each of which details a specific aspect of the electron's configuration: the principal quantum number (n), the azimuthal quantum number (l), the magnetic quantum number (ml), and the spin quantum number (ms).

1. Principal quantum number (n)

The principal quantum number, n, indicates the main energy level or shell in which the electron resides. It is a positive integer (1, 2, 3, ...). The value of n indicates the relative size and energy of the atomic orbitals. The larger the value of n, the greater the distance of the electron from the nucleus, and hence, the larger the atomic orbital.

Principal quantum number (n) n=1 n=2 n=3

For example, in the electron configuration of an atom, you might see signs like these:

1s 2 2s 2 2p 6

Here, 1 and 2 represent the principal quantum number. When n equals 1, it indicates the first shell, and n equals 2 indicates the second shell, and so on.

The number of electrons a shell can hold is given by the following formula:

2n 2

Therefore, the first shell (n = 1) can hold a maximum of 2 electrons, the second shell (n = 2) can hold a maximum of 8 electrons, and so on.

2. Azimuthal quantum number (l)

The azimuthal quantum number, l, also known as the angular momentum quantum number, defines the shape of the orbital. It can take integer values from 0 to n - 1 for each shell.

The values of l correspond to different subshells or types of orbitals. The common nomenclature for these is:

  • l = 0: s-orbital
  • l = 1: p-orbital
  • l = 2: d-orbital
  • l = 3: f-orbital
Azimuthal quantum number (l) s-orbital (l=0) p-orbital (l=1) d-orbital (l=2)

s-orbital is spherical, p-orbital is dumbbell-shaped, and d-orbital can have more complex shapes often described as a cloverleaf.

The azimuthal quantum number l not only characterizes the shape of the orbital but also contributes to the energy of the electron. Within the same principal quantum number, orbitals with different l values have slightly different energy levels.

3. Magnetic quantum number (ml)

The magnetic quantum number, m l, describes the orientation of the orbital in space relative to other orbitals. It can take integer values from -l to +l, including zero.

For example, if l = 1 (a p orbital), then m l can be -1, 0, or +1. This results in three possible orientations for p orbital, often denoted as p x, p y, and p z.

Magnetic quantum number (ML) pz orbital (ml=0)

This quantum number is important in magnetic fields, where it determines the shift in energy levels. Therefore, it is called the "magnetic" quantum number.

4. Spin quantum number (ms)

The spin quantum number, ms, describes the spin of the electron, which can be either +1/2 or -1/2. Electron spin is a fundamental property, like charge or mass, and it gives rise to the magnetic properties of the atom.

In a given orbital, the Pauli exclusion principle states that no two electrons can have the same set of all four quantum numbers. Thus, if there is a pair of electrons in an orbital, their spins must be opposite - one +1/2 and the other -1/2.

Spin quantum number (ms) MS=+1/2 MS=-1/2

Electron spin is important for understanding phenomena such as electron pairing and the chemical reactivity of substances.

Applications of quantum numbers

Quantum numbers are fundamental to understanding the various properties and behaviors of atoms and molecules. They are essential tools for chemists to understand the arrangement of electrons in an atom. Here are some applications:

  • Electron configuration: Quantum numbers allow us to write the electron configuration of atoms, which shows the distribution of electrons among orbitals.
  • Spectroscopy: In spectroscopy, quantum numbers explain spectral lines. Different transitions of electrons between quantized energy levels result in spectral lines that are specific to each element.
  • Chemical bonding: The pairing of electrons, governed by quantum numbers, is important in forming covalent and ionic bonds.
  • Magnetism: Spin quantum number helps explain the magnetic properties of materials. Materials with unpaired electrons exhibit magnetism.

Conclusion

Quantum numbers uniquely identify the location and properties of an electron within an atom. Understanding these concepts provides a better understanding of atomic theory and chemical reactions. This knowledge is the backbone of modern chemistry and plays a vital role in scientific advancements in chemistry, physics, and material science.


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Quantum numbers

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