The World of the Very Small
Quantum mechanics is the fundamental theory in physics that provides a description of the physical properties of nature at the scale of atoms and subatomic particles. It is one of the most successful theories in science.
Quantization and the Photoelectric Effect
Quantum (plural: quanta): A discrete, indivisible packet of a physical quantity like energy or momentum.
Quantization: The concept that physical quantities can only exist in certain discrete amounts, not continuous values.
The Photoelectric Effect: The emission of electrons from a material when light shines on it.
Classical prediction: Any color of light, if intense enough, should be able to eject electrons.
Observation: Only light above a certain threshold frequency could eject electrons, regardless of intensity.
Einstein's Explanation (1905): Light itself is quantized into packets of energy called photons. The energy of a photon is given by E = hf, where h is Planck's constant and f is the frequency. An electron can only be ejected if it is hit by a single photon with enough energy to overcome the material's work function. This was a crucial piece of evidence for the quantum nature of light.
Wave-Particle Duality
This is a central concept of quantum mechanics.
The Principle: Quantum entities like photons and electrons exhibit both wave-like and particle-like properties.
Wave properties: Interference and diffraction.
Particle properties: Position and momentum.
Which behavior is observed depends on the experiment being performed. An electron can act like a billiard ball in one experiment and a wave in another.
The Heisenberg Uncertainty Principle
This principle places a fundamental limit on the precision with which we can know certain pairs of physical properties of a particle.
The Principle: It is impossible to simultaneously know both the position and the momentum of a particle with perfect accuracy.
Δx Δp ≥ ħ/2 (where ħ is the reduced Planck constant)
This is not a limitation of our measuring instruments, but an inherent 'fuzziness' of nature at the quantum scale. The more precisely you measure a particle's position, the less precisely you can know its momentum, and vice-versa.