Atomic Structure, Quantum Numbers, and Periodic Trends: Study Notes

Atomic Structure and Quantum Numbers

Energy Levels and Sublevels in the Hydrogen Atom

The hydrogen atom provides a foundational model for understanding atomic energy levels and orbitals. Each principal energy level (denoted by quantum number n) contains one or more sublevels, which are further divided into atomic orbitals.

• Principal Quantum Number (n): Indicates the main energy level or shell.

• Sublevels: The number of sublevels within a level equals n.

• Orbitals: The number of orbitals within a sublevel is determined by the type of sublevel (s, p, d, f): - s: 1 orbital - p: 3 orbitals - d: 5 orbitals - f: 7 orbitals

• Total Orbitals in a Level: The number of orbitals in a level is $n^2$.

• Degeneracy: In the hydrogen atom, all sublevels within a principal energy level have the same energy and are called degenerate.

Spin Quantum Number (ms)

The spin quantum number describes the magnetic behavior of an electron in an atom. It specifies the orientation of the electron's spin within an orbital.

• Possible Values: $+\frac{1}{2}$ (spin up) or $-\frac{1}{2}$ (spin down)

• Significance: Determines the magnetic properties of atoms and ions.

Shapes of Atomic Orbitals

s Orbitals

Each principal energy level contains one s orbital, which is spherically shaped. The probability of finding an electron decreases exponentially as the distance from the nucleus increases.

• Shape: Spherical

• Probability Density: Highest at the nucleus, decreases with distance

p Orbitals

For angular momentum quantum number $l = 1$, there are three p orbitals (px, py, pz), each with a dumbbell shape oriented along different axes.

• Shape: Dumbbell-shaped, oriented along x, y, and z axes

• Nodes: Locations where the probability of finding an electron is zero

d Orbitals

For $l = 2$, there are five d orbitals, each with more complex shapes, often described as cloverleaf or donut-shaped.

• Shape: Four-lobed or donut-shaped

• Number: Five d orbitals per energy level (starting from n = 3)

f Orbitals

For $l = 3$, there are seven f orbitals, with even more complex shapes.

• Shape: Multi-lobed

• Number: Seven f orbitals per energy level (starting from n = 4)

Energy Ordering of Orbitals in Multi-electron Atoms

General Energy Ordering

In multi-electron atoms, sublevels are not degenerate due to electron-electron repulsion and shielding effects. The energy ordering of orbitals is determined by both the principal quantum number and the type of orbital.

• Order of Filling: Orbitals fill in the order of increasing energy, generally following the sequence: 1s → 2s → 2p → 3s → 3p → 4s → 3d → 4p → 5s → 4d → 5p → 6s → 4f → 5d → 6p → 7s, etc.

• Penetration and Shielding: s orbitals penetrate closer to the nucleus and experience less shielding, making them lower in energy compared to p, d, and f orbitals of the same principal quantum number.

Periodic Trends

Atomic and Ionic Radius

The atomic radius is the distance from the nucleus to the outermost electron shell. Ionic radius refers to the size of an ion compared to its neutral atom.

• Trend Down a Group: Atomic and ionic radii increase due to addition of electron shells.

• Trend Across a Period: Atomic and ionic radii decrease due to increasing effective nuclear charge, pulling electrons closer.

• Cations: Smaller than neutral atoms

• Anions: Larger than neutral atoms

Ionization Energy

Ionization energy is the minimum energy required to remove an electron from an atom or ion in the gas phase. It is an endothermic process.

• First Ionization Energy: $A(g) + IE_1 \rightarrow A^+(g) + e^-$

• Second Ionization Energy: $A^+(g) + IE_2 \rightarrow A^{2+}(g) + e^-$

• Trend Down a Group: Decreases (valence electrons farther from nucleus)

• Trend Across a Period: Increases (effective nuclear charge increases)

• Successive Ionization Energies: Each successive electron removed requires more energy, especially when removing core electrons.

Electron Affinity

Electron affinity is the energy change when a neutral atom gains an electron in the gas phase. It is usually exothermic (negative value), but can be endothermic for some elements.

• General Equation: $A(g) + e^- \rightarrow A^-(g) + EA$

• Trend Down a Group: Electron affinity decreases (less negative)

• Trend Across a Period: Electron affinity increases (more negative)

• Halogens: Group 17 elements have the most negative electron affinities

• Exceptions: Noble gases and some alkaline earth metals have positive (endothermic) electron affinities due to closed sublevels

Electron Affinity Table (Selected Elements)

Group	Element	Electron Affinity (kJ/mol)
1A	Li	60
2A	Be	>0
3A	B	-27
4A	C	-122
5A	N	>0
6A	O	-141
7A	F	-328
8A	Ne	>0

Magnetic Properties of Atoms and Ions

Paramagnetism and Diamagnetism

The magnetic properties of atoms and ions depend on their electron configurations.

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

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

Summary Table: Periodic Properties

Property	Trend Down a Group	Trend Across a Period
Atomic Radius	Increases	Decreases
Ionic Radius	Increases	Decreases
Ionization Energy	Decreases	Increases
Electron Affinity	Decreases	Increases

Example: Fluorine has a high ionization energy and a very negative electron affinity, making it highly reactive and a strong oxidizing agent.

Additional info: The notes above expand on brief points and diagrams, providing full academic context and definitions for key terms and trends in atomic structure and periodic properties.