Quantum Mechanics, Atomic Structure, and Electromagnetic Radiation: Study Notes

Quantum Mechanics and Atomic Structure

Law of Conservation of Energy

The law of conservation of energy states that energy cannot be created or destroyed, but it can be transformed from one form to another.

• Key Point: Energy is conserved in all chemical and physical processes.

• Example: Heat transfer between a hot plate and a piece of iron.

Nature of Light and Waves

Light exhibits wave-like properties, characterized by wavelength and frequency.

• Wavelength (λ): The distance between consecutive peaks of a wave.

• Frequency (ν): The number of wave cycles passing a point per unit time (measured in Hz or s-1).

• Relationship: Wavelength and frequency are inversely related.

• Equation: $c = \lambda \nu$ where $c$ is the speed of light ($2.998 \times 10^8$ m/s).

Units and Conversions

• Wavelength: Typically measured in meters (m) or nanometers (nm).

• Frequency: Measured in Hertz (Hz) or s-1.

• Energy and Frequency: Directly proportional, as described by Planck's equation.

• Equation: $E = h\nu$ where $h$ is Planck's constant ($6.626 \times 10^{-34}$ J·s).

Electromagnetic Spectrum

The electromagnetic spectrum includes all types of electromagnetic radiation, classified by wavelength and frequency.

• Order (increasing frequency): Radio waves < Microwaves < Infrared (IR) < Visible < Ultraviolet (UV) < X-rays < Gamma rays

• Visible Light: Wavelengths from approximately 400 nm (violet) to 700 nm (red).

• Color Perception: Objects appear a certain color because they reflect specific wavelengths and absorb others.

Atomic Emission and Absorption

Atoms absorb energy and electrons move to higher energy levels (excited state). When electrons return to lower energy levels (ground state), they emit photons of light.

• Photon: A quantum of light energy.

• Spectra: The set of wavelengths emitted or absorbed by substances.

• Emission Spectrum of Hydrogen: Specific transitions correspond to UV, visible, or IR light.

Bohr Model and Quantum Numbers

The Bohr model describes electrons in discrete energy levels around the nucleus. Quantum numbers specify the properties of atomic orbitals and electrons.

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

• Sublevels: s (sphere, 2 electrons), p (peanut, 6 electrons), d (clover, 10 electrons), f (complex, 14 electrons).

Electron Configurations and Orbital Diagrams

Electron configurations describe the arrangement of electrons in an atom. Orbital diagrams use arrows to represent electron spins in orbitals.

• Aufbau Principle: Fill the lowest energy orbitals first.

• Pauli Exclusion Principle: Maximum of two electrons per orbital, with opposite spins.

• Hund's Rule: Fill degenerate orbitals singly before pairing electrons.

• Example: $1s^2 2s^2 2p^6 3s^2 3p^5$ for chlorine (Cl).

Identifying Elements from Electron Configurations

Electron configurations can be used to identify elements. For example, $[Ar]4s^2 3d^5$ corresponds to manganese (Mn).

Key Equations and Constants

• Speed of Light: $c = 2.998 \times 10^8$ m/s

• Planck's Constant: $h = 6.626 \times 10^{-34}$ J·s

• Energy of a Photon: $E = h\nu$

• Wavelength-Frequency Relationship: $c = \lambda \nu$

Sample Table: Hydrogen Emission Spectrum

Transition	Type of Light
n=4 → n=3	IR
n=3 → n=2	Visible
n=2 → n=1	UV
n=5 → n=2	Visible
n=6 → n=2	Visible

Sample Table: Electromagnetic Spectrum Classification

Wavelength (m)	Region
2.4 × 102	Radio
6.7 × 10-9	Gamma
8.2 × 10-7	IR
1.2 × 10-12	Gamma
5.8 × 10-2	Microwaves
3.0 × 108	Long Radio Waves

Additional info:

• These notes cover foundational concepts in quantum mechanics, atomic structure, and electromagnetic radiation, which are essential for understanding modern chemistry.

• Sample calculations and electron configurations are included to reinforce key principles.