# Compton Wavelength Calculator

By Miłosz Panfil, PhD
Last updated: Feb 22, 2019

With the Compton wavelength calculator, you can quickly compute the Compton wavelength of any object knowing just its mass. Keep on reading to see what is the Compton wavelength equation and how it relates to a fundamental limitation on measurement.

## Compton wavelength equation

The Compton wavelength of an object, like an elementary particle or an atom, corresponds to a wavelength of a photon of energy equal to the rest energy of this object. The rest energy of an object of mass `m` is `E = m c²`, while the energy of a photon of wavelength `λ` is `E = h c / λ`. Combining these two equations, we find the equation for the Compton wavelength:

`λ = h / (m * c)`,

where

• `h = 6.62607 * 10^(-34) J/s` is the Planck constant,
• `m [kg]` is the mass of an object,
• `c = 299 792 458 m/s` is the speed of light,
• `λ [m]` is the Compton wavelength.

Compton wavelength is a distance at which we should use the Quantum Field Theory instead of simple quantum physics. Quantum Field Theory is a theory which puts quantum physics together with special relativity. One of its predictions is that particles can be created out of the vacuum. The Compton wavelength sets the distance at which such processes are feasible.

## Limitation on measurement

What does the creation of particles from the vacuum have in common with a limitation on measurement? Let us ask where the particle is. To answer the question, we could shine a light on the particle. To be able to localize an object the wavelength of the light should be comparable with the size of the object. If the particle is small, it means that we need to use photons of considerable energy. To see an object, the photon must collide with it. However, if a photon has a lot of energy, the collision might have drastic effects.

For example, if the photon with energy larger than `mc²` strikes an elementary particle of mass `m` (like an electron), it might lead to the creation of particle-antiparticle pairs. If that's the case, the initial question "where is the particle" becomes nonsensical: now we have two particles and one antiparticle. Trying to localize better the particle we made the situation worse. This is the limitation on measurement the Compton wavelength provides.

## Compton wavelength calculator

So what is the Compton wavelength of elementary particles like an electron and a proton? It is easy to answer this question with our calculator.

1. For an electron merely choose the mass units to be electron mass. In this units, the mass of the electron is, well, `1 me`. The resulting Compton wavelength is `2.42631 pm`.

2. For a proton choose the mass units to be proton mass units. The resulting Compton wavelength is `0.0013214 pm`.

De Broglie wavelength is a similar quantity which gives a typical distance in which quantum physics takes over the classical picture.

Miłosz Panfil, PhD
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