# Photon Energy Calculator

In 1905 Einstein, starting from the groundbreaking work by Planck on the black-body radiation, confirmed the **quantization of the energy of a photon**: our photon energy calculator will teach you that fundamental relationship.

In our photon energy calculator you will learn:

**What is a photon**, and why are they so important;- The equation for the
**energy of a photon**: how to calculate the**energy from the frequency**; - How to calculate the
**energy from the wavelength**; and - How to calculate the
**number of photons**in a light beam.

## What is a photon?

A photon is the building block of light. Both a particle (since they carry **De Broglie wavelength** calculator), a photon is the **quanta** of light: you can't find something smaller (less energetic) than a photon and still call it light.

It's hard to talk of photons without terribly understating their importance. They are everywhere, and since they **are** **electromagnetic radiation**, they make up everything, from radio waves to visible light, from microwaves to gamma rays.

A detailed description of photons takes much more time than we have. So, let's be short!

## The quantization of light

At the end of the XIX century, a catastrophe happened in the world of physics. Not a literal one, but the **ultraviolet catastrophe**, an unexplained behavior of the radiation emitted by a **black body**. With a lot of intelligence and a bit of desperation, Max Planck introduced an arbitrary **quantization**, a discretization of the behavior, that fitted both the experimental data and the first modelization given by Wien's law.

A few years later, Einstein, studying the emission of electrons by a material hit by light (the **photoelectric effect**), proved the ideas of Planck right, showing that light arrived on the material in the form of **discrete energy packets**, **quanta**. Einstein didn't stop here and derived the **Planck-Einstein relation** (or **Planck's equation**), which tells us how to calculate the energy of a photon in a few symbols.

## Calculate the energy from the frequency of a photon

Planck's equation first appeared in the calculations of the

from the frequency. It simply states:Where:

- $E$ is the
**energy of a photon**; - $h$ is the
**Planck's constant**; and - $\nu$ is the
**photon's frequency**.

🙋 The Planck's constant has value $h = 6.62607015\cdot 10^{-34}\ \text{J}/\text{{Hz}}$

Let's try the formula for the energy of a photon: let's take a photon with frequency $\nu = 729.422\ \text{THz}$. Apply the Planck-Einstein relation:

This energy is extremely small, and luckily so: this photon is in the visible part of the spectrum, and it would be problematic if it was dangerous to us.

## How to calculate the energy of a photon: energy from wavelength calculations

Frequency and wavelength are intimately related by the velocity of the wave in the medium. When talking about photons, the velocity is $c$, a fundamental constant in physics. Knowing that $\nu = \tfrac{c}{\lambda}$, where $\lambda$ is the wavelength, we can derive the equation of the energy of a photon from the wavelength:

Now that you know how to calculate the energy from the wavelength and the frequency let's scale up from a single photon to multiple ones.

## Calculations for more than a photon

Since light is quantized, we can calculate the number of photons in a light beam of given energy and frequency by simply dividing the energy of the beam by the result of the formula for the energy of a photon: