Planck constant
Introduction
The Planck constant (denoted as "h") is a fundamental physical constant that plays a pivotal role in quantum mechanics, the theory that provides our best description of the microscopic world of atoms and subatomic particles. It is named after Max Planck, a German theoretical physicist who is considered the father of quantum theory.
Historical Background
Max Planck introduced the constant in 1900 during his research on black-body radiation. The introduction of the Planck constant was a revolutionary step in physics, marking the birth of quantum mechanics. Planck's work on black-body radiation led to the development of the quantum hypothesis, which states that energy is quantized, i.e., it can only exist in discrete amounts.
Physical Significance
The Planck constant has dimensions of energy multiplied by time, which are the dimensions of action. In the International System of Units (SI), it is expressed in joule-seconds (J·s). The Planck constant is a fundamental constant because it sets the scale for the quantum mechanical effects that become significant when action is on the order of the reduced Planck constant (ℏ = h/2π).
Role in Quantum Mechanics
In quantum mechanics, the Planck constant is the proportionality constant between the energy (E) of a photon and the frequency (ν) of its associated electromagnetic wave. This relation between the energy and frequency is called the Planck–Einstein relation: E = hν.
The Planck constant also appears in the Heisenberg uncertainty principle, which states that the uncertainty in the position (Δx) and momentum (Δp) of a particle cannot both be precisely determined at the same time. The product of these uncertainties is at least on the order of the reduced Planck constant: ΔxΔp ≥ ℏ/2.
Measurement and Value
The value of the Planck constant has been measured with increasing accuracy over the years. As of the May 20, 2019 redefinition of the SI units, the Planck constant is defined to be exactly 6.62607015×10−34 J·s. This exact value was chosen so that the speed of light and the charge of the electron, which are also fundamental physical constants, could retain their previous definitions.
Implications and Applications
The Planck constant has far-reaching implications in physics and beyond. It is essential in the study of quantum mechanics and is used in a variety of calculations. For example, it is used to calculate the energy levels of atoms in the Bohr model, and it appears in the Schrödinger equation, the fundamental equation of quantum mechanics.
Moreover, the Planck constant also has practical applications. For instance, it is used in the definition of the kilogram, the SI unit of mass. Since May 20, 2019, the kilogram has been defined by setting the Planck constant to an exact value, rather than by a physical artifact.