Overview
This lecture introduces electromagnetic waves, explaining their properties, how they are generated, and their relationship to charged particles and energy levels.
Properties of Electromagnetic Waves
- Electromagnetic waves are disturbances that carry energy from one place to another.
- Key characteristics of waves: amplitude, wavelength, and frequency.
- They travel at the speed of light, which is (3 \times 10^8) meters per second.
- Speed of light ((c)) = wavelength ((\lambda)) × frequency ((f)): (c = \lambda \times f).
- When wavelength decreases, frequency increases (inverse relationship).
- Frequency is the number of cycles per second (measured in Hertz, Hz).
- Period is the time for one cycle (measured in seconds), and frequency is inversely related to period.
- The energy of an electromagnetic wave is given by (E = h \times f), where (h) is Planck’s constant ((6.626 \times 10^{-34}) J·s).
Structure of Electromagnetic Waves
- Electromagnetic waves are made of oscillating electric and magnetic fields.
- Electric ((E)) and magnetic ((B)) fields oscillate perpendicular to each other and the direction of wave propagation.
- Changing electric fields create changing magnetic fields and vice versa.
- The electric field strength equals the speed of light multiplied by the magnetic field strength ((E = cB)).
Generation of Electromagnetic Waves
- Any charged particle has an electric field around it.
- A moving charged particle creates a magnetic field.
- An accelerating charged particle produces electromagnetic waves.
Electromagnetic Wave Emission in Atoms
- When electrons move from a higher to a lower energy level in an atom, they emit electromagnetic waves (photons).
- The energy of emitted photons in hydrogen is (E = -2.18 \times 10^{-18} \text{J} \left( \frac{1}{n_{f}^2} - \frac{1}{n_{i}^2} \right)), where (n_f) and (n_i) are final and initial energy levels.
- Absorbing a photon allows an electron to jump to a higher energy state; releasing a photon occurs when it falls to a lower state.
Other Ways to Emit Electromagnetic Waves
- Oscillating electrons in metals (e.g., when heated) emit electromagnetic waves.
- Hot metals glow red, yellow, or white as electrons emit more energetic waves with increasing temperature.
- Any accelerating charged particle can emit electromagnetic waves.
Key Terms & Definitions
- Wave — A disturbance that carries energy from one place to another.
- Wavelength ((\lambda)) — The distance between consecutive crests or troughs in a wave.
- Frequency ((f)) — Number of cycles per second, measured in Hertz (Hz).
- Period — Time for one full cycle of a wave, measured in seconds.
- Electromagnetic Wave — A wave composed of oscillating electric and magnetic fields that propagates at the speed of light.
- Planck’s Constant ((h)) — (6.626 \times 10^{-34}) joule·seconds, relates energy and frequency.
- Photon — A particle of light or electromagnetic radiation.
Action Items / Next Steps
- Review the formulas for wave speed, energy, and photon emission in atoms.
- Practice problems on wavelength, frequency, and energy calculations.
- Read the next section on the electromagnetic spectrum.