Electromagnetic Spectrum — Frequency, Wavelength & Energy
Calculate frequency, wavelength, and photon energy for any part of the electromagnetic spectrum using E=hf and c=fλ.
Electromagnetic Spectrum Guide
The Relationships: c=fλ and E=hf
Two key equations connect all EM wave properties. Wave equation: c = f × λ. Where c = speed of light (3×10⁸ m/s), f = frequency (Hz), λ = wavelength (m). Rearranged: f = c/λ and λ = c/f. Energy: E = h × f. Where h = Planck's constant (6.626×10⁻³⁴ J·s), f = frequency. In eV: E(eV) = hf/e where e = 1.6×10⁻¹⁹ C. Combined: E = hc/λ. Example: green light at 500nm. f = 3×10⁸/(500×10⁻⁹) = 6×10¹⁴ Hz. E = 6.626×10⁻³⁴ × 6×10¹⁴ = 3.98×10⁻¹⁹ J = 2.48 eV.
The EM Spectrum Regions
Radio waves (λ > 1mm, f < 3×10¹¹ Hz): TV, FM/AM radio, WiFi, mobile phones. Microwaves (1mm-1m): microwave ovens, radar, satellite communication. Infrared (700nm-1mm): thermal imaging, remote controls, TV remotes, optical fibre. Visible light (400-700nm): violet 400nm, blue 450nm, green 550nm, yellow 580nm, red 700nm. Ultraviolet (10-400nm): UV-A, UV-B (sunburn), UV-C (sterilisation). X-rays (0.01-10nm): medical imaging, security scanners. Gamma rays (< 0.01nm): nuclear radiation, cancer treatme
Photon Energy and the Photoelectric Effect
Einstein explained the photoelectric effect (Nobel Prize 1921) using the particle nature of light — photons. When light hits a metal surface, electrons are ejected only if photon energy E ≥ work function Φ (a property of the metal). KE_max = hf − Φ. Below a threshold frequency f₀ = Φ/h, no electrons are emitted regardless of intensity. This proved light behaves as packets of energy (quanta) — not continuous waves. The threshold frequency for sodium is approximately 5.5×10¹⁴ Hz (in the yellow-gre
Wave-Particle Duality
All electromagnetic radiation exhibits both wave properties (diffraction, interference, polarisation) and particle properties (photoelectric effect, Compton scattering). The de Broglie wavelength: all particles with momentum p have an associated wavelength λ = h/p. Electrons: de Broglie wavelength of electrons in an electron microscope ≈ 0.001 nm — far smaller than visible light, allowing atomic-resolution imaging. This wave-particle duality is fundamental to quantum mechanics and led to the dev
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