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Quantum Mechanics and Periodic Properties: Electrons, Orbitals, and the Periodic Table

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Electromagnetic Radiation and the Electromagnetic Spectrum

Nature of Electromagnetic Radiation

Electromagnetic radiation is a form of energy that travels through space as waves. It includes radio waves, microwaves, infrared, visible light, ultraviolet (UV), x-rays, and gamma rays. All electromagnetic radiation moves at the speed of light, which is m/s.

  • Wavelength (λ): The distance between two consecutive crests or troughs of a wave.

  • Frequency (ν): The number of wave crests passing a point per second.

  • Relationship: The speed of light is the product of wavelength and frequency:

  • Visible Light: Occupies wavelengths from 700 nm (red) to 400 nm (violet).

  • Energy: As frequency increases, wavelength decreases, and energy increases.

Light passing through a prism and wavelength illustration Electromagnetic spectrum diagram

Atomic Spectra and Energy Levels

Photons and Atomic Spectra

Light is emitted as photons, which are particles of electromagnetic radiation. When elements are excited, they emit light at specific wavelengths, producing atomic spectra unique to each element. These spectral lines correspond to changes in electron energy levels.

  • Energy Levels: Electrons occupy specific energy levels, denoted by the principal quantum number n (1–7).

  • Excited State: When an electron absorbs energy equal to the difference between energy levels, it moves to a higher energy level.

  • Relaxation: When the electron returns to a lower energy level, it emits a photon.

Atomic spectra for strontium and barium Bookcase analogy for energy levels Energy absorption and photon emission diagram

Sublevels and Orbitals

Structure of Energy Levels

Each energy level contains sublevels designated as s, p, d, and f. These sublevels contain orbitals, which are regions where electrons are likely to be found. The maximum number of electrons in each energy level is determined by the formula .

  • Sublevels: s (1 orbital), p (3 orbitals), d (5 orbitals), f (7 orbitals).

  • Orbital Shapes: s is spherical, p is dumbbell-shaped, d and f have more complex shapes.

  • Electron Capacity: Each orbital holds 2 electrons with opposite spins.

Energy Level (n)

2n2

Maximum Number of Electrons

1

2(1)2

2

2

2(2)2

8

3

2(3)2

18

4

2(4)2

32

Maximum number of electrons table Shapes of p orbitals Shapes of d orbitals

Orbital Diagrams and Electron Configurations

Representing Electron Arrangements

Electron arrangements can be shown using orbital diagrams (boxes and arrows) or electron configurations (notation). Lower energy orbitals fill first, and electrons occupy separate orbitals of the same energy before pairing (Hund’s Rule).

  • Electron Configuration: Indicates the distribution of electrons among orbitals, e.g., for carbon:

  • Abbreviated Configuration: Uses noble gas notation for elements beyond neon, e.g., for sodium.

Periodic table blocks for electron configuration Electron configuration for carbon

Element

Atomic Number

Orbital Diagram (3s and 3p only)

Electron Configuration

Abbreviated Electron Configuration

Na

11

[Ne] 3s1

1s22s22p63s1

[Ne] 3s1

Mg

12

[Ne] 3s2

1s22s22p63s2

[Ne] 3s2

Electron configuration table for Na and Mg

Electron Configurations and the Periodic Table

Periodic Table Blocks and Filling Order

The periodic table is divided into s, p, d, and f blocks, which correspond to the filling of orbitals. The filling order is determined by orbital energies, with exceptions for certain elements (e.g., Cr, Cu, Mo, Ag).

  • Filling Order: 4s fills before 3d due to lower energy.

  • Exceptions: Some elements promote electrons to half-fill or fill d orbitals.

Periodic table blocks diagram

Trends in Periodic Properties

Valence Electrons, Atomic Size, Ionization Energy, and Metallic Character

Periodic properties are determined by electron arrangements and energy levels. The group number indicates the number of valence electrons. Atomic size, ionization energy, and metallic character show predictable trends across periods and groups.

  • Atomic Size: Increases down a group (more shells), decreases across a period (greater nuclear charge).

  • Ionization Energy: Energy required to remove an electron; decreases down a group, increases across a period.

  • Metallic Character: Tendency to lose electrons; increases down a group, decreases across a period.

Atomic size trend diagram Ionization energy and metallic character trend diagrams

Summary Table: Periodic Trends

Property

Trend Down a Group

Trend Across a Period

Atomic Size

Increases

Decreases

Ionization Energy

Decreases

Increases

Metallic Character

Increases

Decreases

Additional info: The notes cover quantum mechanics, atomic structure, electron configurations, and periodic properties, which are central to General Chemistry topics.

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