Atomic Structure and Spectroscopy

Hydrogen Emission Spectrum and Electron Transitions

The hydrogen atom emits light when an electron transitions from a higher energy level to a lower one. The energy difference between these levels determines the wavelength and color of the emitted light.

• Energy Levels: Electrons in hydrogen occupy discrete energy levels, labeled by the principal quantum number n.

• Transition: When an electron falls from a higher energy level (e.g., n = 6) to a lower one (e.g., n = 5), it emits a photon.

• Energy of Transition: The energy difference is given by:

• Wavelength Calculation: The wavelength of the emitted photon is: where is Planck's constant and is the speed of light.

• Example: For a transition from n = 6 to n = 5:

  • Calculate using the formula above.

  • Find using .

  • The resulting wavelength falls in the visible spectrum, specifically in the violet range.

Key Terms: Photon, Wavelength, Visible Spectrum, Quantum Number

Electron Configuration and Periodic Trends

Valence Electrons and Element Identification

Valence electrons are the outermost electrons of an atom and determine its chemical properties.

• Valence Electron Configuration: The configuration ns2np4 indicates 6 valence electrons.

• Possible Elements: Elements with this configuration include oxygen, sulfur, and selenium.

• Example: Oxygen: 1s22s22p4

Formulas of Ionic Compounds

Nonmetals with 6 valence electrons typically form 2- anions. Potassium (K) forms 1+ cations. The formula for the compound formed is:

• General Formula: (for oxygen), (for sulfur)

Periodic Trends: Atomic Radius and Ionization Energy

• Atomic Radius: Decreases across a period (left to right) and increases down a group.

• Comparison: Nonmetals (right side) have smaller radii than metals (left side) in the same period.

• Ionization Energy: The energy required to remove an electron from an atom. Increases across a period and decreases down a group.

• Example: Oxygen has a higher ionization energy than barium, but lower than fluorine.

Quantum Numbers and Atomic Orbitals

Quantum Numbers

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

• Principal Quantum Number (n): Indicates the energy level (n = 1, 2, 3, ...).

• Angular Momentum Quantum Number (l): Indicates the shape of the orbital (l = 0 for s, 1 for p, 2 for d, 3 for f).

• Magnetic Quantum Number (ml): Indicates the orientation of the orbital (ranges from -l to +l).

• Spin Quantum Number (ms): Indicates the spin of the electron (+1/2 or -1/2).

Allowed Quantum Number Combinations

• For n = 3, l = 2, ml = -2, -1, 0, 1, 2 (d orbitals)

• For n = 4, l = 1, ml = -1, 0, 1 (p orbitals)

• For n = 2, l = 1, ml = 0, ms = +1/2 or -1/2

Electron Configurations and the Periodic Table

Writing Electron Configurations

Electron configurations describe the arrangement of electrons in an atom's orbitals. The Aufbau principle, Pauli exclusion principle, and Hund's rule guide the order in which orbitals are filled.

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

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

• Hund's Rule: Electrons occupy degenerate orbitals singly before pairing.

Examples of Electron Configurations

• Arsenic (As), Group 5A: [Ar] 4s2 3d10 4p3

• Element 116 (Livermorium, Lv): [Rn] 5f14 6d10 7s2 7p4

• Osmium (Os) with three unpaired 5d electrons: [Xe] 4f14 5d6 6s2

• Halogen with electrons in the 6p atomic orbitals (Astatine, At): [Xe] 4f14 5d10 6s2 6p5

Table: Quantum Numbers and Orbital Types

Summary of Key Concepts

• Electron transitions in hydrogen produce visible light with specific wavelengths.

• Valence electron configurations help identify elements and predict their chemical behavior.

• Quantum numbers define the properties and allowed states of electrons in atoms.

• Electron configurations are determined by the order of orbital energies and the rules of quantum mechanics.

• Periodic trends such as atomic radius and ionization energy are predictable based on position in the periodic table.