# Compare the wavelengths of a photon and an electron

• chef99
In summary, photons and electrons are both fundamental particles in the universe with distinct properties. Photons are particles of light, while electrons are negatively charged particles that make up atoms. They differ in mass, charge, and behavior. Photons and electrons also have different wavelengths, with photons having much smaller wavelengths due to their lack of mass and ability to travel at the speed of light. The wavelength of a photon determines its energy and how it interacts with matter, while the wavelength of an electron affects its behavior in quantum mechanics. Both photons and electrons can change their wavelengths through various processes and their wavelengths can be measured using different techniques.
chef99

## Homework Statement

Compare and contrast a 2.2 eV photon with a 2.2 eV electron in terms of wavelength (m).[/B]

p = h/λ

λ = h/mv

## The Attempt at a Solution

For photon:

p = h/λ

λ = h/p

λ = (6.63 x10-34) / (1.17 x10-27kgm/s)**

λ = 5.67 x10-7 m

**I have already determined the momentum as is just one part of the question, in which the energy, momentum, rest mass and velocities are calculated.

For electron:

λ = h/mv

λ = (6.63 x10-34) / (9.11 x10-31kg)(8.8 x105m/s)

λ = 8.27 x10-10 m
I am confident in my answers, I am just curious as to why the wavelength for the electron is smaller than that of the photon, as I would have assumed the wavelength of the photon would be smaller, due to its greater velocity. I thought smaller wavelength means a higher frequency, which, in turn, means the wave is moving faster? However, this cannot be the case as the photon is obviously moving faster. I'd appreciate any explanation as I haven't been able to find one. This is, of course, assuming I've done my calculations correctly but I think I have. Thanks

chef99 said:

## Homework Statement

Compare and contrast a 2.2 eV photon with a 2.2 eV electron in terms of wavelength (m).[/B]

p = h/λ

λ = h/mv

## The Attempt at a Solution

For photon:

p = h/λ

λ = h/p

λ = (6.63 x10-34) / (1.17 x10-27kgm/s)**

λ = 5.67 x10-7 m

**I have already determined the momentum as is just one part of the question, in which the energy, momentum, rest mass and velocities are calculated.

For electron:

λ = h/mv

λ = (6.63 x10-34) / (9.11 x10-31kg)(8.8 x105m/s)

λ = 8.27 x10-10 m
I am confident in my answers, I am just curious as to why the wavelength for the electron is smaller than that of the photon, as I would have assumed the wavelength of the photon would be smaller, due to its greater velocity. I thought smaller wavelength means a higher frequency, which, in turn, means the wave is moving faster? However, this cannot be the case as the photon is obviously moving faster. I'd appreciate any explanation as I haven't been able to find one. This is, of course, assuming I've done my calculations correctly but I think I have. Thanks
Your calculations are correct. When speaking of the energy of the electron, it usually means the kinetic energy, From an electron and a photon of the same energy, the electron has greater momentum, and shorter wavelength. That is the basics of the electron microscopes
"An electron microscope is a microscope that uses a beam of accelerated electrons as a source of illumination. As the wavelength of an electron can be up to 100,000 times shorter than that of visible light photons, electron microscopes have a higher resolving power than light microscopes and can reveal the structure of smaller objects.ˇ" (Wikipedia)
The wavelength is inversely proportional to the momentum.
The momentum p=mv both for the electron and the photon, if m is the relativistic mass. For kinetic energies as low as a few eV, the mass of the electron is 9.1x10-31kg.
Because of the mass-energy relationship E=mc2, you can attribute the mass E/c2 to the photon, and now it is much less than the mass of the electron. In spite of the greater velocity, the momentum of the photon is smaller than that of the electron.

Last edited:
chef99
You seem to have a couple of common misconceptions about waves, so here's a few things to think about.
chef99 said:
I am confident in my answers, I am just curious as to why the wavelength for the electron is smaller than that of the photon, as I would have assumed the wavelength of the photon would be smaller, due to its greater velocity.
Consider two photons with different energies. They both move at the speed of light yet they have different wavelengths. You don't want to relate speed to wavelength.

I thought smaller wavelength means a higher frequency, which, in turn, means the wave is moving faster?
Again, consider two photons with different frequencies. Both move at the same speed.

Also think about a wave on a string. Its speed is given by ##v = \sqrt{T/\mu}## where ##T## is the tension in the string and ##\mu## is the mass per unit length. The speed doesn't depend on wavelength or frequency.

However, this cannot be the case as the photon is obviously moving faster. I'd appreciate any explanation as I haven't been able to find one. This is, of course, assuming I've done my calculations correctly but I think I have. Thanks
For both a photon and an electron, you have ##\lambda = h/p##, so the difference in the wavelengths is due to the fact they have different momenta. For a photon, the energy and momentum are related by
$$p_\gamma = \frac{E}{c} = \frac{\sqrt{E^2}}c.$$ For a non-relativistic electron, you have
$$p_e = \sqrt{2mE} = \frac{\sqrt{2(mc^2)E}}{c} = \frac{\sqrt{2E_0 E}}c,$$ where ##E_0## is the rest energy of the electron. Comparing the expressions for the momentum of the photon and the electron, you can see that the rest energy of the electron causes the momentum of the electron to grow more quickly with energy than the momentum of the photon does, resulting in a shorter wavelength for the same kinetic energy.

chef99

## 1. What is the difference between a photon and an electron?

Photons and electrons are both fundamental particles in the universe, but they have distinct properties. A photon is a particle of light, while an electron is a negatively charged particle that makes up atoms. They differ in mass, charge, and behavior.

## 2. Do photons and electrons have the same wavelength?

No, photons and electrons have different wavelengths. The wavelength of a photon is determined by its frequency, while the wavelength of an electron is determined by its momentum. Photons have much smaller wavelengths than electrons, as they have no mass and can travel at the speed of light.

## 3. How do the wavelengths of photons and electrons affect their behavior?

The wavelength of a photon determines its energy and how it interacts with matter. Shorter wavelengths have higher energy and can penetrate deeper into matter. On the other hand, the wavelength of an electron affects its behavior in quantum mechanics. Electrons can behave like waves and exhibit interference patterns, making their wavelength an important factor in their behavior.

## 4. Can the wavelength of a photon or an electron be changed?

Yes, the wavelength of both photons and electrons can be changed. Photons can change their wavelength through processes like refraction, diffraction, and scattering. Electrons can also change their wavelength through interactions with other particles, such as in the Compton effect.

## 5. How are the wavelengths of photons and electrons measured?

The wavelengths of photons are typically measured using tools such as spectrometers or diffraction gratings. For electrons, their wavelength can be measured using techniques like electron diffraction or the de Broglie wavelength equation, which relates the wavelength of a particle to its momentum.

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