Maxwell's Theory and Hertz's Experiment

• Maxwell's theory unified electricity and magnetism, predicting electromagnetic waves that travel at the speed of light.

Classical Electromagnetism and Hertz’s Experiment

• Hertz experimentally confirmed Maxwell’s prediction of electromagnetic waves.
• The transmitter used an induction coil connected to spheres, generating oscillations via short voltage pulses.
• The receiver consisted of a wire loop connected to spheres, placed meters away.
• Energy transfer occurred when transmitter and receiver resonance frequencies matched.
• Hertz found that electromagnetic waves had properties similar to light waves.
• The measured speed of these waves closely matched the speed of light (3 x 10^8 m/s).
• Electromagnetic waves are produced by accelerating charged particles, such as in an antenna with alternating current.
• Electromagnetic waves are transverse, with electric (E) and magnetic (B) fields perpendicular to each other and to the direction of propagation.
• The speed of light © is 3 x 10^8 m/s.
• Light functions as an electromagnetic wave.

Blackbody Radiation

• A blackbody absorbs all incident radiation and re-emits it based on temperature.
• Blackbodies absorb all wavelengths of light.
• Blackbodies emit radiation at every wavelength, dependent on temperature, which is referred to as blackbody radiation.
• A blackbody emits a specific radiation spectrum at a given temperature where the intensity of the radiation changes at different wavelengths.
• The peak emission wavelength decreases as temperature increases (Wien’s Displacement Law).
• Total emitted energy increases with temperature (Stefan-Boltzmann Law).
• The peak shifts toward shorter wavelengths (e.g., infrared to visible light) at higher temperatures.
• Classical physics predicted infinitely increasing radiation intensity at shorter wavelengths, contradicting observations which resulted in the ultraviolet catastrophe.
• Max Planck proposed energy is quantized, emitted/absorbed in discrete packets (quanta).
• Planck’s Law: E = hf, where h is Planck’s constant (6.63 x 10^-34 Js).
• Energy quantization resolved the ultraviolet catastrophe.

The Photoelectric Effect

• The photoelectric effect occurs when light strikes a metal surface, emitting electrons (photoelectrons).
• No electrons are emitted if light frequency is below a cutoff frequency.
• The maximum kinetic energy of emitted electrons relies on the light frequency, not intensity.
• Electrons are emitted almost instantaneously, even at low light intensities.
• Classical wave theory failed to explain the cutoff frequency, kinetic energy independence from light intensity, and instantaneous emission.
• Einstein stated that light is made up of discrete energy packets known as photons.
• Photon energy is given by E = hf, with h as Planck's constant and f as the frequency of light.
• Photoelectric Equation: KE_max = hf - Φ, where Φ is the work function.
• No electrons are emitted if hf < Φ.
• Electrons are emitted if hf > Φ, with kinetic energy KE_max = hf - Φ.
• Photocells convert light into electrical current, used in streetlights, garage door openers, and elevators.

X-Rays

• X-rays are electromagnetic radiation with short wavelengths (around 0.1 nm).
• They were discovered by Wilhelm Roentgen in 1895.
• X-rays have high energy, allowing penetration through most materials.
• They are used in medical diagnostics, security, and material inspection.
• X-rays are produced by decelerating high-speed electrons striking a metal target.
• Electrons emitted from a heated filament are accelerated toward a metal target.
• When electrons collide with the target, they emit X-rays and lose energy.
• The continuous spectrum (Bremsstrahlung) results from electrons losing energy in multiple collisions.
• Sharp peaks in the characteristic spectrum correspond to specific energy transitions.
• Crystals can diffract x-rays, allowing study of crystal structures.
• Bragg’s Law: 2d sin θ = mλ, where d is crystal plane spacing, θ is the angle of incidence, and λ is the X-ray wavelength.

The Compton Effect

• The Compton Effect is when X-rays scatter by electrons, their wavelength increases (Compton shift).
• Scattered X-rays have longer wavelengths than incident X-rays.
• The wavelength shift depends on the scattering angle.
• Photons transfer momentum and energy to electrons during collisions.
• Change in wavelength: Δλ = λ' - λ = h/(m_e c) * (1 - cos θ), where λ' is the scattered photon wavelength, λ is the initial wavelength, and θ is the scattering angle.
• Compton Wavelength: λ_c = h/(m_e c) = 0.00243 nm.
• The Compton effect is strong proof of the particle nature of light (photons).

Summary

• Light demonstrates wave-particle duality through interference, diffraction, the photoelectric effect, and Compton scattering.
• Quantum Theory states that energy is quantized, light interacts with matter as photons.
• Hertz’s experiment confirmed electromagnetic waves.
• Planck’s quantization resolved the ultraviolet catastrophe.
• Einstein’s photoelectric effect explained electron emission using photons.
• The Compton Effect proved the particle nature of light.