Planck's constant
Introduction
Planck's constant (denoted as h) is a fundamental physical constant that plays a pivotal role in the theory of quantum mechanics. Named after the German physicist Max Planck, who first proposed it in 1900, this constant is central to the development of quantum theory and has profound implications for our understanding of the physical universe.
History
The constant was first introduced by Max Planck during his study of black-body radiation. Planck was trying to solve the so-called 'ultraviolet catastrophe' problem in classical physics, which predicted that a black body would emit infinite energy at ultraviolet frequencies. This was in stark contrast to experimental observations. Planck found that by assuming energy was quantized, or came in discrete packets (which he called 'quanta'), he could accurately describe the observed black-body radiation spectrum. This assumption led to the introduction of Planck's constant, which is the proportionality constant between the energy of a photon and its frequency.
Value and Units
The value of Planck's constant is approximately 6.62607015 × 10^-34 joule-seconds (J·s) in the International System of Units (SI). It is a dimensionful constant, meaning it has physical units. The smallness of Planck's constant reflects the fact that on human scales, the energy levels of systems appear continuous, not quantized.
Significance in Quantum Mechanics
Planck's constant is a cornerstone of quantum mechanics. It appears in several fundamental equations, including the Schrödinger equation, which describes the wave-like behavior of particles, and the Heisenberg uncertainty principle, which states that the position and momentum of a particle cannot both be precisely known at the same time.
In quantum mechanics, the energy E of a photon (a quantum of light) is given by the equation E = hν, where ν is the frequency of the photon. This equation, known as the Planck-Einstein relation, shows that the energy of a photon is quantized, with the smallest possible energy being hν. This quantum nature of light is a direct consequence of Planck's constant.
Planck Units
Planck's constant also plays a key role in defining the Planck units, a system of natural units that is particularly useful in theoretical physics. In this system, Planck's constant is set to 1, which simplifies many equations. The Planck units are derived from the fundamental constants of nature: Planck's constant, the speed of light, the gravitational constant, the Coulomb constant, and Boltzmann's constant.
Recent Developments
In 2019, the International System of Units (SI) was redefined so that Planck's constant, along with the speed of light and the charge of the electron, are now defined to have exact values. This change was made to increase the precision of scientific measurements and to make the definitions of the units more consistent with the fundamental principles of physics.