Modern Physics
E=mc², photoelectric · 8 formulas
Mass-Energy Equivalence
Mass is a highly concentrated form of energy; the speed of light squared is the conversion factor.
Lorentz Factor
As speed approaches c, time stretches and lengths contract by the factor γ.
Photoelectric Effect
Light comes in quanta of energy hν; only photons above the work-function threshold can free electrons.
De Broglie Wavelength
Every particle has a wavelength inversely proportional to its momentum — heavy/fast things have wavelengths so small they're unobservable.
Heisenberg Uncertainty Principle
Position and momentum cannot both be sharply defined; nature enforces a fundamental fuzziness at small scales.
Schrödinger Equation (Time-Independent)
The total energy operator acting on the wavefunction returns the energy times the same wavefunction — an eigenvalue problem for reality.
Bohr Energy Levels (Hydrogen)
Electrons in hydrogen are stuck on a ladder of negative energies; the gaps determine the colors of light atoms emit.
Radioactive Decay Law
Each nucleus has a fixed probability per unit time of decaying, producing a smooth exponential decline in the population.