Planck’s Constant: Formula & Application

After watching this lesson, you will be able to explain what Planck’s constant is and use the Planck-Einstein relation to calculate the energy in a photon of light. A short quiz will follow.
What Is Planck’s Constant?
Planck’s constant is a number that describes the size of the energy packets (or ‘quanta’) that are contained within light. These packets of energy are called photons. Planck’s constant is given the symbol h in physics and numerically is equal to 6.63 x 10^-34 Joule seconds.

Towards the end of the 19th century, Planck was working to understand black-body radiation — a kind of radiation that would be emitted by a perfect absorber and emitter of radiation. This is very close to the kind of radiation we receive from the sun. Planck successfully created an equation to describe black-body radiation, but then realized his solution was one of many, which could lead to many different values of energy produced.

In a last-ditch attempt to make his ideas work, he proposed that the energy of light was not a continuous quantity — you couldn’t just have absolutely any value of energy. Rather, light must contain packets of energy of a particular size. Although it was an act of desperation, he turned out to be right and won a Nobel Prize in 1918 for his work.

Equation
While Planck’s constant can now be found in many equations, the equation that defines Planck’s constant is called the Planck-Einstein relation, and it looks like this: E = hf.

Here, E is the energy of each packet (or ‘quanta’) of light, measured in Joules; f is the frequency of light, measured in hertz; and h is of course Planck’s constant. So the constant describes how to take the frequency (or color) of light and use it to determine the size of the packets of energy (or photons) it contains.

It’s a pretty straight-forward equation, but one that was part of a revolution in physics. Understanding the existence of these ‘quanta’ led over the following few decades to the development of quantum mechanics, a topic that has revolutionized physics and, in turn, led to huge advances in the world.

Example
Let’s go through an example. Let’s say you’re shining blue light of frequency 6.2 x 10^14 hertz on a piece of metal, causing electrons to be produced from the surface. How much energy does each photon of light contain?

To solve this, we just plug numbers into the Planck-Einstein relation. We know the frequency is 6.2 x 10^14, and Planck’s constant is always 6.63 x 10-34. The energy is just h multiplied by f, so multiply those two numbers together, and we get 4.1 x 10^-19 Joules. And that’s it. That’s our answer.