**Planck’s constant** is one of the fundamental constants in physics that sets the scale for quantum effects. It is the proportionality constant that relates the energy of a photon to the frequency of its corresponding electromagnetic wave. The symbol for Planck’s constant is *h*. It is also known as the Planck constant.

### Value of Planck’s Constant in SI Units

In SI units, the value of Planck’s constant is defined:

*h* = 6.62607015×10^{−34} m²·kg/s = 6.62607015×10^{−34} J·Hz^{-1} = 6.62607015×10^{−34} J·s

### Value of Planck’s Constant in eV

In terms of electron volts (eV), the value is approximately:

*h* = 4.135667696×10^{−15} eV·s

### Significance and Importance

Planck’s constant is pivotal in the realm of quantum mechanics, the branch of physics dealing with the behavior of particles at the atomic and subatomic levels. Without Planck’s constant, quantum theory would be mathematically incoherent. It sets the scale for a multitude of phenomena, from the behavior of electrons in atoms to the properties of the early universe.

### Relating Photon Energy and Wave Frequency

Planck’s constant *h* relates the energy *E* of a photon to the frequency of its corresponding electromagnetic wave *f*:

*E* = *h*⋅*f*

By relating frequency and wavelength λ, the equation becomes:

*E* = *h*⋅*c / *λ

### The Dirac Constant or Reduced Planck Constant

The Dirac constant or reduced Planck constant ℏ (h-bar) is *h*/2*π*. Dividing Planck’s constant by 2π makes it easier working in radians rather than hertz. This constant is especially useful when dealing with angular momentum in quantum systems. The value of ℏ in SI units is approximately 1.0545718×10^{−34} m²·kg/s. It plays a crucial role in the Schrödinger equation, which governs how quantum systems evolve over time.

### History

The constant was first postulated by Max Planck in 1900. He introduced it to explain the ultraviolet catastrophe, a divergence in the predictions of classical physics when describing the electromagnetic spectrum of radiation in a black body. With the introduction of *h*, Planck provided a groundbreaking solution that laid the groundwork for quantum theory.

Max Planck received the Nobel Prize in Physics in 1918 for his discovery of the energy quanta, which essentially laid the foundation for quantum theory. His introduction of the Planck constant revolutionized our understanding of atomic and subatomic processes. The Nobel Prize recognized the immense significance of his work, which marked a watershed moment in the history of physics and set the stage for the development of quantum mechanics. Planck’s work deeply influenced subsequent generations of physicists and led to groundbreaking theories and applications, ranging from quantum mechanics to quantum field theory and beyond.

### Relation to the Photoelectric Effect

Albert Einstein used the concept of Planck’s constant to explain the photoelectric effect in 1905. He showed that light could be thought of as a stream of photons, each with energy *E*=*h*⋅*f*. This explanation won Einstein the Nobel Prize in Physics in 1921 and provided early experimental evidence in favor of quantum theory.

### Atomic Structure

The Bohr model of the hydrogen atom was one of the first applications of Planck’s constant in atomic physics. The quantization of angular momentum in the model is directly related to Planck’s constant, and this quantization explains phenomena like atomic spectra.

### Heisenberg Uncertainty Principle

The Heisenberg Uncertainty Principle, formulated by Werner Heisenberg in 1927, states that the position *x* and the momentum *p* of a particle cannot both be known exactly at the same time. The principle is mathematically represented as:

Δ*x*Δ*p* ≥ ℏ/2

Here, Δ*x* and Δ*p* are the uncertainties in position and momentum, respectively, and ℏ is the reduced Planck constant.

### Fixed Definition

In 2019, the International Committee for Weights and Measures redefined the kilogram in terms of Planck’s constant, thereby “fixing” its value. This redefinition is significant because it provides a stable and universal basis for mass, which was previously based on a physical artifact. This makes all of the SI base units defined.

### Determining Planck’s Constant Before 2019

Before 2019, Planck’s constant was determined through experiments like the Kibble balance and Josephson voltage standards, along with comparisons to the mass of the International Prototype of the Kilogram. A 2011 experiment at the Large Hadron Collider also determined the value of the Planck constant experimentally.

### Additional Facts

- Planck’s constant also appears in the expression for the energy levels of a quantum harmonic oscillator.
- It is used to calculate the Planck length, time, and mass, which are the scales below which the classical notions of space, time, and mass cease to exist.
- Planck units, derived using Planck’s constant along with other fundamental constants, provide a natural unit system particularly useful for cosmology and high-energy physics.

### References

- Barrow, John D. (2002).
*The Constants of Nature; From Alpha to Omega – The Numbers that Encode the Deepest Secrets of the Universe*. Pantheon Books. ISBN 978-0-375-42221-8. - Einstein, Albert (2003). “Physics and Reality”.
*Daedalus*. 132 (4): 24. doi:10.1162/001152603771338742 - International Bureau of Weights and Measures (2019).
*Le Système international d’unités*[*The International System of Units*] (in French and English) (9th ed.). ISBN 978-92-822-2272-0. - Kragh, Helge (1999).
*Quantum Generations: A History of Physics in the Twentieth Century*. Princeton University Press. ISBN 978-0-691-09552-3. - Planck, Max (1901). “Ueber das Gesetz der Energieverteilung im Normalspectrum”.
*Ann. Phys*. 309 (3): 553–63. doi:10.1002/andp.19013090310