Chapter 7 – Electromagnetic Radiation & Quantum Theory

Electromagnetic Radiation

Visible light is a type of EM radiation.

Wave Properties

Described by frequency (ν), wavelength (λ), and speed (c).

Frequency (ν)

Cycles per second

Wavelength (λ)

Distance of one wave cycle

Speed

Wave travel speed in m/s

Amplitude

Height of crest/depth of trough

Speed of Light

c = 3.00 × 10⁸ m/s

c = λν

Speed = wavelength × frequency

Unit of Frequency

Hertz (Hz) = s⁻¹

Blackbody Radiation

Hot solids emit light; color depends on temperature.

Energy-Frequency-Wavelength

Energy ∝ frequency ∝ 1/wavelength

Photon Energy

E = hν or E = hc/λ

Planck’s Constant

h = 6.626 × 10⁻³⁴ J·s

Quantum Number (n)

Integer values only (1, 2, 3…)

Line Spectra

Excited gases emit specific colors/lines.

Rydberg Equation

ν = (RH/h)(1/ni² – 1/nf²); ΔE = RH(1/ni² – 1/nf²)

Rydberg Constant

R_H = 2.18 × 10⁻¹⁸ J

Bohr Model

Electrons in specific energy levels; photons emitted/absorbed during transitions.

Allowed H Energy Levels

En = –RH / n²

Zero-Point Energy

E = 0 when n = ∞ (ionized electron)

Electron Emission

Electron drops to lower energy, emits photon.

Electron Absorption

Electron jumps to higher energy, absorbs photon.

Other 1-e⁻ Systems

En = –RH(Z²/n²) for hydrogen-like ions

Quantum Mechanical Model

Electron behaves as wave; described by wavefunctions.

Probability Density

|ψ|² gives likelihood of finding electron.

Atomic Orbital

Described by quantum numbers n, l, m_l.

Principal Quantum Number (n)

Indicates orbital size/energy.

Angular Momentum Quantum Number (l)

Defines shape; l = 0 (s), 1 (p), 2 (d), 3 (f).

Magnetic Quantum Number (m_l)

Orientation: –l to +l.

Degenerate Orbitals

Same-n orbitals in hydrogen have same energy.

Energy Splitting

Multi-electron atoms have sublevel energy differences.

Sublevel Energy Order

s < p < d < f < g within same n level.