# Electron frequency and wavelength

• new_id_7
In summary, the conversation discusses the de Broglie wavelength of an electron and its relationship to its momentum and energy. While the frequency for a photon is equal to the speed of light divided by its wavelength, the frequency for an electron is tied to its energy rather than its wavelength. This is due to a careful analysis of the roles of phase velocity and group velocity for particles with mass. The correct relationship for an electron is f = E/h.
new_id_7
Hi, I'm studying the wave nature of particles.

My book says that the de broglie wavelength of an electron is h / momentum, or h / (mv).
I also have that E = hf = momentum2/(2m) = 1/2 mv2.
I know that for a photon the frequency is speed of light / wavelength.

I'm wondering why the frequency for an electron is not 1/ wavelength. Is there any equation relating f and lambda for a particle (electron)?

Thanks for any help.

DeBroglie predicted the wavelength of matter waves would be the same as for the photon.
The releatonship you want is the one you stated: f = c/lambda

Experimental confirmation is discussed here:
http://en.wikipedia.org/wiki/DeBroglie_wavelength

Naty's answer seems very wrong to me. The wavelength of a particle is tied to its momentum. The frequency is related to its energy. When you combine the wavelength and frequency to get the apparent velocity of the electron, the answer comes out wrong. You don't get the correct velocity.

The resolution of this paradox comes from a careful analysis of the roles of phase velocity vs. group velocity.

Naty1 said:
The releatonship you want is the one you stated: f = c/lambda

If c is the speed of light, that works only for photons.

For particles with mass, $f = v_{phase} / \lambda$ which gives

$$v_{phase} = f \lambda = \left( \frac{E}{h} \right) \left( \frac{h}{p} \right) = \frac{E}{p} = \frac {\sqrt{(pc)^2 + (m_0 c^2)^2}}{p}$$

Duh, seems wrong to me, too; right your guys are!..I should have posted f = E/h
the equations are right there in the wiki reference, too.

## 1. What is the relationship between electron frequency and wavelength?

The frequency and wavelength of an electron are inversely proportional. This means that as the frequency increases, the wavelength decreases, and vice versa. This relationship is described by the equation: frequency = speed of light / wavelength.

## 2. How does the energy of an electron relate to its frequency and wavelength?

The energy of an electron is directly proportional to its frequency. This means that as the frequency increases, the energy of the electron also increases. The energy of an electron is also inversely proportional to its wavelength, meaning that as the wavelength decreases, the energy increases. This relationship is described by the equation: energy = Planck's constant * frequency.

## 3. What is the difference between the frequency and wavelength of an electron compared to other particles?

The frequency and wavelength of an electron are unique to the particle itself and cannot be compared to other particles. This is because each particle has its own unique mass and charge, which affects its frequency and wavelength. Additionally, the properties of an electron, such as its wave-particle duality, make it behave differently than other particles.

## 4. How does the electron's frequency and wavelength affect its behavior?

The frequency and wavelength of an electron determine its behavior, particularly in the field of quantum mechanics. The wave-like behavior of an electron, described by its frequency and wavelength, can affect its interactions with other particles and its ability to pass through barriers. Additionally, the energy of an electron, which is determined by its frequency and wavelength, plays a crucial role in chemical reactions and electron transitions.

## 5. Can the frequency and wavelength of an electron be measured?

Yes, the frequency and wavelength of an electron can be measured using various techniques such as spectroscopy. These measurements provide valuable information about the properties and behavior of electrons in different systems, and have led to many advancements in the field of physics.

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