Electronic Structure of Atoms and Periodic Properties

Electronic Structure of Atoms

Waves and Electromagnetic Radiation

Understanding the electronic structure of atoms requires knowledge of electromagnetic radiation, which behaves as waves and travels at the speed of light.

• Electromagnetic radiation: Energy that moves through space as waves.

• Wavelength (λ): The distance between corresponding points on adjacent waves.

• Frequency (ν): The number of waves passing a given point per unit time.

• For waves at the same velocity, longer wavelength means lower frequency.

• Relationship: As wavelength decreases, frequency increases.

Equation:

$c = \lambda \nu$

Where c is the speed of light (3.00 × 108 m/s).

The Photoelectric Effect

Einstein explained the photoelectric effect using the concept of quanta. Electrons are emitted from metal surfaces when light of sufficient energy shines on them.

• Each metal has a threshold energy for electron ejection.

• Energy is proportional to frequency:

$E = h\nu$

Where h is Planck's constant (6.626 × 10-34 J·s).

Bohr Model and Energy Transitions

The Bohr model describes energy transitions in atoms:

• Absorption: A positive ΔE means energy is absorbed (photon absorbed), $n_f > n_i$.

• Emission: A negative ΔE means energy is released (photon emitted), $n_f < n_i$.

Heisenberg Uncertainty Principle

Heisenberg showed that the more precisely the momentum of a particle is known, the less precisely its position is known.

$(\Delta x)(\Delta mv) \geq \frac{h}{4\pi}$

Where Δx is the uncertainty in position and Δmv is the uncertainty in momentum.

Quantum Mechanics and Wave Functions

Schrödinger's wave equation for hydrogen yields wave functions for the electron. The square of the wave function gives the electron density, or the probability of finding an electron at a given location.

Quantum Numbers and Orbitals

Solving the wave equation gives a set of wave functions (orbitals) and their energies. Each orbital is described by four quantum numbers:

• n: Principal quantum number (energy level)

• l: Angular momentum quantum number (orbital shape)

• ml: Magnetic quantum number (orbital orientation)

• ms: Spin quantum number (electron spin)

Electron Shells and Subshells

Orbitals with the same value of n form an electron shell. Different orbital types within a shell are subshells.

n	Subshell Designation	Possible l	Possible ml	Number of Orbitals	Total Orbitals in Shell
1	1s	0	0	1	1
2	2s, 2p	0, 1	0; -1,0,1	1; 3	4
3	3s, 3p, 3d	0, 1, 2	0; -1,0,1; -2,-1,0,1,2	1; 3; 5	9
4	4s, 4p, 4d, 4f	0, 1, 2, 3	0; -1,0,1; -2,-1,0,1,2; -3,-2,-1,0,1,2,3	1; 3; 5; 7	16

Pauli Exclusion Principle

No two electrons in the same atom can have the same set of four quantum numbers. Thus, each electron in an atom must differ by at least one quantum number.

Electron Configurations

The arrangement of electrons in an atom is its electron configuration. The most stable (lowest energy) arrangement is the ground state.

• Format: energy level (number), orbital type (letter), number of electrons (superscript).

• Example: $4p^5$

Orbital Diagrams

Orbital diagrams visually represent electron configurations:

• Each box = one orbital

• Half-arrows = electrons

• Arrow direction = electron spin

Hund's Rule

When filling degenerate orbitals (orbitals of the same energy), the lowest energy is achieved when the number of electrons with the same spin is maximized. Each orbital in a sublevel gets one electron before any pairing occurs.

Electron Configurations of Lighter Elements

Element	Total Electrons	Orbital Diagram	Electron Configuration
Li	3	1s: ↑↓, 2s: ↑	1s22s1
Be	4	1s: ↑↓, 2s: ↑↓	1s22s2
B	5	1s: ↑↓, 2s: ↑↓, 2p: ↑	1s22s22p1
C	6	1s: ↑↓, 2s: ↑↓, 2p: ↑ ↑	1s22s22p2
N	7	1s: ↑↓, 2s: ↑↓, 2p: ↑ ↑ ↑	1s22s22p3
O	8	1s: ↑↓, 2s: ↑↓, 2p: ↑↓ ↑ ↑	1s22s22p4
Ne	10	1s: ↑↓, 2s: ↑↓, 2p: ↑↓ ↑↓ ↑↓	1s22s22p6
Na	11	1s: ↑↓, 2s: ↑↓, 2p: ↑↓ ↑↓ ↑↓, 3s: ↑	1s22s22p63s1

Condensed Electron Configurations

Elements in the same group have the same number of valence electrons. The filled inner shell electrons are called core electrons. Condensed electron configurations use brackets for noble gases and list only valence electrons.

Periodic Properties of the Elements

Sizes of Atoms and Ions

Atomic and ionic sizes are important periodic properties.

• Atomic radius: Half the distance between nuclei in a bond (covalent radius) or during a collision (van der Waals radius).

• Ionic size: Depends on nuclear charge, orbital location, and number of electrons.

• Cations are smaller than parent atoms; anions are larger.

Isoelectronic Series

Ions with the same number of electrons form an isoelectronic series. Ionic size decreases as nuclear charge increases.

Ion	Protons	Electrons	Radius (Å)
O2-	8	10	1.26
F-	9	10	1.19
Na+	11	10	1.16
Mg2+	12	10	0.86
Al3+	13	10	0.68

Ionization Energy

Ionization energy is the minimum energy required to remove an electron from a gaseous atom or ion.

• First ionization energy: Energy to remove the first electron.

• Second ionization energy: Energy to remove the second electron.

• It requires more energy to remove each successive electron.

• Core electrons require much higher ionization energy than valence electrons.

Electron Affinity

Electron affinity is the energy change when an electron is added to a gaseous atom. It is typically exothermic (negative value).

• Highest electron affinity: Chlorine (Cl).

• Equation: $\mathrm{Cl} + e^- \rightarrow \mathrm{Cl}^-$

Metals, Nonmetals, and Metalloids

Elements are classified based on their properties:

• Metals: Good conductors, malleable, ductile, tend to lose electrons.

• Nonmetals: Poor conductors, brittle, tend to gain electrons.

• Metalloids: Properties intermediate between metals and nonmetals.

Basic Concepts of Chemical Bonding

Lattice Energy

Lattice energy is the energy required to completely separate one mole of a solid ionic compound into its gaseous ions.

• Released when the ionic compound forms (Born-Haber cycle).

• Example: $\mathrm{NaCl}(s) \rightarrow \mathrm{Na}^+(g) + \mathrm{Cl}^-(g)$, $\Delta H_{\text{lattice}} = +788\ \mathrm{kJ/mol}$

Trends in Lattice Energy

• Lattice energy increases with increasing charge and decreasing size of ions.

$E_{el} = \frac{k Q_1 Q_2}{d}$

Where $Q_1$ and $Q_2$ are ion charges, $d$ is separation distance, and $k$ is a proportionality constant.

Covalent Bonding and Bond Polarity

Covalent bonds involve sharing electrons between nonmetals. Bond polarity measures how equally electrons are shared.

• Nonpolar covalent bond: Electrons shared equally.

• Polar covalent bond: Electrons shared unequally; one atom attracts electrons more strongly.

Lewis Structures

Lewis structures show how atoms share electrons to achieve noble gas configurations. Each bond contains two electrons.

• Steps: Sum valence electrons, connect atoms, complete octets, place remaining electrons, use multiple bonds if needed.

Resonance

Some molecules cannot be accurately depicted by a single Lewis structure. Resonance structures are used to represent delocalized electrons (e.g., ozone, benzene).

Exceptions to the Octet Rule

• Odd number of electrons (e.g., NO)

• Fewer than eight electrons (e.g., BF3)

• More than eight electrons (expanded octet, e.g., PF5, phosphate)

Bond Enthalpy and Bond Length

• Multiple bonds are stronger and shorter than single bonds.

• Bond length decreases as the number of bonds increases.