Planck constant

The Planck constant, denoted by h, is one of the most important numbers in science. It helps us understand how tiny particles, like atoms and photons (particles of light), behave. In quantum mechanics, the energy of a photon is linked to its frequency, and this link is made possible by the Planck constant.

This constant was first introduced by physicist Max Planck in 1900. He needed it to explain how objects give off heat and light, a process known as black-body radiation. Later, Albert Einstein used this idea to explain the nature of light itself. For his work, Max Planck was awarded the 1918 Nobel Prize in Physics.

Today, the Planck constant is more than just a number—it is used to define the kilogram, one of the basic units of measurement. Its exact value is 6.62607015×10⁻³⁴ J⋅Hz⁻¹, and it helps scientists measure tiny amounts of energy and matter with great precision. Another version, called the reduced Planck constant (ℏ or "h-bar"), is often used in equations to make calculations easier.

History

Origin of the constant

Main article: Planck's law

The Planck constant was created by Max Planck in 1900. He was trying to solve a problem about how objects give off light, called black-body radiation. At the time, scientists had some ideas about this, but none worked perfectly.

Planck came up with a new idea: he thought that light energy could only come in certain small "packets" or chunks. This helped him create a formula that matched what scientists saw in experiments. This formula included a special number, which we now call the Planck constant. It shows how much energy light has based on its frequency.

Development and application

In 1905, scientists found that old ideas about light could not explain some experiments. This helped everyone understand that Planck’s idea about energy packets was very important. His work led to big changes in how we think about physics.

Photoelectric effect

Main article: Photoelectric effect

The photoelectric effect happens when light shines on a metal surface and causes electrons to come off. Before Einstein’s work, people thought of light as a wave. But Einstein suggested that light is made of tiny packets called photons. He showed that the energy of these photons depends on the light’s frequency, not its brightness. This idea matched experiments and helped prove that light can act like particles.

Atomic structure

Main article: Bohr model

Scientists used the Planck constant to explain how electrons move around atoms. They found that electrons can only have certain energy levels, which match what the Planck constant helps describe.

Uncertainty principle

Main article: Uncertainty principle

The Planck constant also helps explain a big idea in quantum physics: you can’t always know both where a particle is and how fast it’s moving at the exact same time. The more precisely you know one thing, the less precisely you can know the other. This is called the uncertainty principle.

Photon energy

The Planck constant connects the energy of a photon (a particle of light) to its frequency. This means that higher frequency light has more energy.

de Broglie wavelength

Later, scientists found that the Planck constant also works for other tiny particles, not just light. It helps describe a special wavelength related to moving particles.

Statistical mechanics

The Planck constant shows up in theories about how groups of particles behave. It helped scientists understand that certain things in nature can only take on specific values, not any value at all.

Dimension and value

The Planck constant has the same size as action and angular momentum. We measure it in joule-seconds (J·s). Its exact value is 6.62607015×10⁻³⁴ J⋅Hz⁻¹. This value helps define the SI unit of mass, the kilogram.

Because the Planck constant is very small, quantum effects only matter when dealing with very tiny amounts of energy and time. For example, a single photon of green light has an extremely small amount of energy—much smaller than what we normally feel in daily life. But when we look at large numbers of these tiny particles, the energy becomes noticeable, like the food energy in an apple.

Reduced Planck constant

The reduced Planck constant, also called the Dirac constant, is a special version of the Planck constant. It is used in many quantum physics equations. It is equal to the Planck constant divided by 2π, and is written as ℏ (pronounced "h-bar").

This special version of the constant was first used by Niels Bohr in 1913. Later, in 1926, Erwin Schrödinger and Paul Dirac introduced their own symbols for it. Dirac chose the symbol ℏ in 1930 in his book The Principles of Quantum Mechanics.