1: Atoms and orbitals

Atoms and Orbitals

Atoms are the fundamental building blocks of matter, composed of a nucleus (protons and neutrons) surrounded by electrons. In chemical reactions, electron behavior dictates bonding and reactivity. Electrons occupy specific regions called atomic orbitals, defined by quantum mechanical principles.

Quantum Numbers

Each electron is described by four quantum numbers:

1. Principal quantum number ($n$): Indicates energy level/shell ($n = 1, 2, 3, \ldots$). Higher $n$ values denote larger orbitals farther from the nucleus.
2. Azimuthal quantum number ($l$): Defines orbital shape (subshell). Values range from $0$ to $n-1$:
   • s orbitals ($l = 0$): Spherical, one orbital per shell.
   • p orbitals ($l = 1$): Dumbbell-shaped, three mutually perpendicular orbitals ($p_x$, $p_y$, $p_z$).
   • d orbitals ($l = 2$) and f orbitals ($l = 3$) are higher-energy shapes (less common in organic molecules).
3. Magnetic quantum number ($m_l$): Specifies orbital orientation (e.g., $m_l = -1, 0, +1$ for p orbitals).
4. Spin quantum number ($m_s$): Denotes electron spin ($+\frac{1}{2}$ or $-\frac{1}{2}$).

Orbital Shapes and Energy

• s orbitals: Spherical symmetry, highest electron density at the nucleus.
• p orbitals: Nodal plane (zero electron density) at the nucleus; lobes extend along axes. Crucial for $\pi$ bonding in organic compounds.
  Orbitals within the same shell (e.g., $2p_x$, $2p_y$, $2p_z$) are degenerate (equal energy) in isolated atoms. Energy increases with $n$ and $l$.

Electron Configuration

Electrons fill orbitals following three rules:

1. Aufbau principle: Orbitals fill from lowest to highest energy (e.g., $1s \to 2s \to 2p$).
2. Pauli exclusion principle: Each orbital holds $\leq 2$ electrons with opposite spins.
3. Hund’s rule: Electrons occupy degenerate orbitals singly before pairing.

Example configurations:

• Carbon ($6e^-$): $1s^2 2s^2 2p^2$ (two unpaired p electrons).
• Oxygen ($8e^-$): $1s^2 2s^2 2p^4$ (two paired p electrons, two unpaired).

Relevance to Organic Chemistry

• s and p orbitals hybridize to form bonds (e.g., $sp^3$ in methane).
• Unpaired electrons in p orbitals enable covalent bonding (e.g., C–H bonds).
• Electron distribution in orbitals explains atomic reactivity and molecular geometry.

Understanding orbitals provides the basis for molecular structure, hybridization, and bonding mechanisms in organic molecules.