General Chemistry: Atomic Structure, Electron Configuration, and Periodic Trends Study Notes

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:

$[Kr] 5s^2 4d^{10} 5p^2$

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: $1s$, $2s$, $2p$, $3s$, $3p$, $4s$, $3d$, $4p$, etc.

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

$1s^2\ 2s^2\ 2p^6\ 3s^2\ 3p^3$

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 $|m_l| \leq l$ and $m_s = \pm 1/2$ are valid.

Periodic Trends and Properties

Isoelectronic Species

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

• Example: $Zn^{2+}$ is isoelectronic with $Cu^+$, $Ni$, $Br^-$, and $Ge^{2+}$.

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 $Ca^{2+}$ and $Sc^{2+}$, $Ca^{2+}$ 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 ($Z_{eff}$) experienced by an electron in a multi-electron atom.

• Effective nuclear charge: $Z_{eff} = Z - S$

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

Example: To find $Z_{eff}$ for a 4p electron in Ga (Gallium):

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

• Calculate $S$ and subtract from $Z$ to get $Z_{eff}$.

Tables

Quantum Number Sets: Allowed vs. Not Allowed

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

Set	n	l	ml	ms	Allowed?
A	3	1	1	+1/2	Yes
B	2	2	0	+1/2	No (l cannot be equal to or greater than n)
C	4	3	-3	-1/2	Yes
D	3	2	2	+1/2	Yes
E	1	0	0	+1/2	Yes
F	2	1	-1	+1/2	Yes

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