Modern Physics Calculators — Quantum, Relativity & Nuclear Decay
Calculate photon energy (E = hf), de Broglie wavelength, relativistic energy (E = mc²), and radioactive decay half-life for quantum and nuclear physics.
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Understanding Modern Physics
Modern physics emerged in the early 20th century when classical physics could not explain phenomena at atomic scales and near-light speeds. Einstein's E = mc² revealed that mass and energy are interchangeable — converting just 1 kg of matter releases 9 × 10¹&sup6; J, enough to power a city for years. This mass-energy equivalence is the foundation of nuclear energy, where fission of uranium-235 converts about 0.09% of its mass into energy.
Quantum mechanics introduced wave-particle duality and quantized energy levels. Photon energy (E = hf) explains why ultraviolet light causes sunburn but visible light does not — UV photons carry enough energy (3-10 eV) to break molecular bonds. The de Broglie wavelength (λ = h/mv) shows that all matter has wave properties, though they are only observable at atomic scales. Radioactive decay follows exponential half-life mathematics that predict exactly how much of a substance remains after any given time.
Modern physics builds on classical optics & light by explaining light's dual nature. It also extends energy conservation to include mass-energy equivalence, showing that the total mass-energy of an isolated system is always conserved even in nuclear reactions.