# Calculating the frequency of a free electron

• Turukano26
In summary, the conversation discusses the calculation of an electron's frequency using different equations. The factor of two in the equation f = mv2/2h is explained as the difference between phase and group velocities of the free electron. This concept is further explained in Griffiths' "Introduction to Quantum Mechanics".
Turukano26
I feel like I must be missing something obvious, but I can't figure it out. I have the speed of an electron, and to calculate its frequency i used p = h/λ, then subbed in p =mv and λ= v/f. Giving me the equation f = mv2/h. However, I also could use E = 1/2 mv2 and E = hf to give me the equation f = mv2/2h. Where is this factor of two coming from??

I am not entirely sure, but I think you have discovered the difference between phase and group velocities of the free electron.And, they are different. Griffiths has a great section on this (Griffiths "Introduction to Quantum Mechanics", Sec 2.4, Eq. 2.90).

Before proceeding you must tell us which "speed" do you mean. The phase velocity, or the group velocity.

sophiecentaur

## 1. How is the frequency of a free electron calculated?

The frequency of a free electron can be calculated using the formula f = E/h, where f is the frequency in hertz, E is the energy of the electron in joules, and h is Planck's constant (6.626 x 10^-34 joule seconds).

## 2. What is the significance of calculating the frequency of a free electron?

Calculating the frequency of a free electron is important in understanding the behavior of electrons in various materials and in the study of quantum mechanics. It can also provide information about the energy levels of an atom or molecule.

## 3. Can the frequency of a free electron be measured experimentally?

Yes, the frequency of a free electron can be measured experimentally using techniques such as spectroscopy or electron microscopy. These methods involve analyzing the interactions between electrons and other particles or electromagnetic waves.

## 4. What factors can affect the frequency of a free electron?

The frequency of a free electron can be affected by the material it is in, the electric and magnetic fields present, and the temperature of the environment. It can also be influenced by the electron's energy and its interactions with other particles.

## 5. How is the frequency of a free electron related to its wavelength?

The frequency of a free electron and its wavelength are inversely proportional. This means that as the frequency increases, the wavelength decreases, and vice versa. This relationship is described by the equation f = c/λ, where c is the speed of light in a vacuum and λ is the wavelength.

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