It's important to include the units: h = 6.63e-34 kg m^2 /s
You can think of the units as being units of position (meters) times momentum (kilogram-meters per second). The value of h might be most easily understood based on its fundamental role in the uncertainty principle. Loosely stated, the uncertainty principle says that if we measure a particle's position to some accuracy A (measured in meters) and simultaneously its momentum to some accuracy B (measured in kilogram-meters per second), then we must have A*B > h. Thus, given A or B there is a minimum value of the other. If I measure the position of a particle to within 1 millimeter, there is a minimum uncertainty in its momentum of h/(1 millimeter) or about 6.6e-31 kg*m/s. This is of course a tiny uncertainty, because h is such a tiny number, at least when expressed in familiar units like kg, m, and s.
If we don't care about knowing any momenta to this precision (e.g. in analyzing the flight of a baseball) we can use classical mechanics and forget quantum effects entirely. But once we start looking at very small scales and investigating things like the position and momenta typical of electrons in atoms, the uncertainty principle starts placing important bounds, and thus quantum effects become important. So the value of h tells you when quantum mechanics is important, or when it isn't and you can use classical mechanics.
Planck's constant, often denoted as "h" and symbolized as ℎ, is a fundamental constant in physics. It is named after the German physicist Max Planck, who introduced it in 1900 as part of his work on the quantum theory of radiation. Planck's constant plays a pivotal role in the field of quantum mechanics and is fundamental to our understanding of the behavior of subatomic particles and the quantization of energy.
Here's what Planck's constant represents and why it's significant:
- Quantization of Energy: Planck's constant is intimately related to the idea that energy is quantized, meaning it exists in discrete, indivisible units or "quanta." This was a groundbreaking departure from classical physics, where energy was considered continuous.
- Relationship to Frequency: Planck's constant is related to the energy of a photon (a particle of light) and its frequency (ν) through the equation E = hν. This equation states that energy is directly proportional to the frequency of a photon, and the constant of proportionality is Planck's constant.
- Explanation of Blackbody Radiation: Planck's constant was first introduced by Max Planck to explain the spectral distribution of blackbody radiation. His theory showed that by assuming energy levels were quantized in integer multiples of hν, he could accurately describe the observed behavior of such radiation.
- Heisenberg's Uncertainty Principle: Planck's constant is one of the key components in Heisenberg's uncertainty principle, a fundamental concept in quantum mechanics. This principle states that there is a fundamental limit to how precisely certain pairs of properties (like position and momentum) of a particle can be simultaneously known. The uncertainty principle relies on the concept of quantized energy levels.
- Units: Planck's constant has units of energy multiplied by time, which can be expressed as joule-seconds (J·s) in the International System of Units (SI). In quantum mechanics, it's often more convenient to work with the reduced Planck's constant (ħ), which is h divided by 2π. The reduced Planck's constant appears frequently in equations involving angular momentum and wavefunctions.
- Value: The value of Planck's constant in SI units is approximately 6.62607015 × 10⁻³⁴ J·s. This value is extremely small, underscoring the tiny size of individual quantum energy levels.
Planck's constant is one of the most important constants in physics because it bridges the gap between classical physics, which describes the macroscopic world, and quantum mechanics, which describes the behavior of particles at the atomic and subatomic scale. It fundamentally altered our understanding of nature and has had far-reaching implications in fields such as quantum physics, atomic physics, and materials science.
