Atomic Structure and Electron Configuration

Electron Configuration

Electron configuration describes the arrangement of electrons in an atom's orbitals. It follows the Aufbau principle, Hund's rule, and the Pauli exclusion principle.

• Aufbau Principle: Electrons fill orbitals starting from the lowest energy level to the highest.

• Hund's Rule: Every orbital in a subshell is singly occupied before any orbital is doubly occupied.

• Pauli Exclusion Principle: No two electrons in an atom can have the same set of four quantum numbers.

• Noble Gas Core Notation: Electron configurations can be abbreviated using the previous noble gas in brackets, followed by the remaining configuration.

Example: The electron configuration for Tin (Sn, Z = 50) is:

Orbital Diagrams

Orbital diagrams visually represent the arrangement of electrons in orbitals using boxes (for orbitals) and arrows (for electrons).

• Each box represents an orbital; arrows represent electrons with spin up (↑) or spin down (↓).

• Orbitals are filled in order of increasing energy: , , , , , , , , etc.

Example: The orbital diagram for Phosphorus (P, Z = 15):

In the 3p subshell, each of the three electrons occupies a separate orbital (Hund's rule).

Quantum Numbers

Quantum numbers describe the properties of atomic orbitals and the electrons in them:

• Principal quantum number (n): Energy level (n = 1, 2, 3, ...)

• Angular momentum quantum number (l): Subshell (l = 0 to n-1; s=0, p=1, d=2, f=3)

• Magnetic quantum number (ml): Orientation (-l to +l)

• Spin quantum number (ms): Electron spin (+1/2 or -1/2)

Allowed Sets: Only combinations where and are valid.

Periodic Trends and Properties

Isoelectronic Species

Isoelectronic species have the same number of electrons but may have different nuclear charges.

• Example: is isoelectronic with , , , and .

Atomic and Ionic Radii

Atomic radius is the distance from the nucleus to the outermost electron shell. Ionic radius refers to the size of an ion.

• Atomic radius decreases across a period (left to right) due to increasing nuclear charge.

• Atomic radius increases down a group due to additional electron shells.

• For isoelectronic ions, the more positive the charge, the smaller the radius.

Example: Arrange O, S, P, K, Cl, F by increasing atomic radius:

• Order: F < O < Cl < S < P < K

Comparing Ionic Radii: For isoelectronic ions such as and , has a larger radius because it has fewer protons (lower nuclear charge) for the same number of electrons.

Paramagnetism and Diamagnetism

These properties describe how substances respond to magnetic fields:

• Paramagnetic: Atoms or ions with unpaired electrons; attracted to magnetic fields.

• Diamagnetic: Atoms or ions with all electrons paired; weakly repelled by magnetic fields.

Example: Selenium (Se) is paramagnetic if it has unpaired electrons in its electron configuration.

Effective Nuclear Charge (Zeff)

Slater's Rules

Slater's rules provide a method to estimate the effective nuclear charge () experienced by an electron in a multi-electron atom.

• Effective nuclear charge:

• is the atomic number, is the shielding constant calculated using Slater's rules.

Example: To find for a 4p electron in Ga (Gallium):

• Write the electron configuration and group electrons according to Slater's rules.

• Calculate and subtract from to get .

Tables

Quantum Number Sets: Allowed vs. Not Allowed

The following table summarizes which sets of quantum numbers are allowed:

Additional info: Set B is not allowed because for n=2, l can only be 0 or 1 (not 2).