Planck's Quantum Theory

Planck's Quantum Theory 2025: E = hν, h=6.626×10⁻³⁴ Js, Lasers, LEDs, $1T Quantum Tech

E = hν • h=6.626×10⁻³⁴ Js • BLACKBODY RADIATION • LASERS/LEDs/QUANTUM COMPUTING

❓ Planck's Constant Value?

h = 6.626 × 10⁻³⁴ J⋅s. 1900 blackbody radiation: E = nhν solves ultraviolet catastrophe. Foundation of quantum mechanics, lasers, semiconductors.

Planck's Quantum Equation

Blackbody radiation: E = hν where h = 6.626 × 10⁻³⁴ J⋅s, ν = frequency. Solves Rayleigh-Jeans ultraviolet catastrophe. Energy quantized: Eₙ = nhν, n = 1,2,3…

Wavelength	Frequency	Photon Energy	Application
650nm Red	461 THz	1.92 eV	Laser Pointers
532nm Green	564 THz	2.33 eV	CD Players
405nm Blue	740 THz	3.06 eV	Blu-ray

Quantum theory enables fiber optics, quantum computing, photovoltaics.

Blackbody Radiation Engineering

Planck's law: B(ν,T) = (2hν³/c²) × 1/(e^(hν/kT)-1). Peak wavelength: λ_max × T = 2.897×10⁻³ m⋅K (Wien's law). LED efficiency 70% vs incandescent 5%.

Semiconductor Bandgap Engineering

GaAs: Eg = 1.42 eV (870nm IR). Si: Eg = 1.12 eV (1100nm). GaN: Eg = 3.4 eV (365nm UV). Direct bandgap enables lasers. Quantum well lasers: 99% wall-plug efficiency at 100mW.

Material	Bandgap	Wavelength	Efficiency
GaN LED	Eg = 3.4 eV	365nm UV	70%
GaAs Laser	Eg = 1.42 eV	870nm	60%
Silicon	Eg = 1.12 eV	1100nm	25%

Quantum Technology Market 2025

Technology	Market	Growth	Applications
LED/Laser	$250B	12%/yr	Displays/Communications
Quantum Computing	$50B	45%/yr	AI/Drug Discovery
Photovoltaics	$200B	18%/yr	Solar Energy

Max Planck Engineering Legacy

1900: Introduces E = hν solving blackbody crisis. 1918 Nobel Prize. Enables $1T quantum tech industry. Schrödinger/Heisenberg quantum mechanics, Einstein photoelectric effect build on Planck's foundation.