# Energy, time and length corresponding to mass of electron.

• H_Psi
In summary, the conversation is about the basics of QED and the units and scales used in calculations. The exercise is to estimate the energy, time, and length corresponding to the mass of an electron. The participant used the equations E=mc^2 and c * hbar = 197 MeV * fm to calculate the energy and length, respectively. The result for the length was questioned, as it may be more accurate to use the Planck constant rather than the reduced Planck constant. The use of hbar as the base unit in calculations is also mentioned as a convention.
H_Psi
Hey,
I am starting to learn the basics of QED and I am trying to get acquainted with the units and scales that are used.

## Homework Equations

The exercise is to estimate the energy, time and length that correspond to the mass of an electron.

## The Attempt at a Solution

That’s what I did:
The mass of an electron is 9.11E-31 kg.

Energy:
E=mc^2 gives me an energy of 0.511MeV.

Length:
Here I used the equation: c * hbar = 197 MeV * fm
-> 386fm = c * hbar / (0.511MeV)
-> In natural units: 386fm = 1 / (0.511MeV)

Time:
Here I used the equation: hbar = 6.58E-22 MeV * s
-> 1.288E-21 s = hbar / (0.511MeV)
-> In natural units: 1.288E-21 s = 1 / (0.511MeV)

Is this calculation correct? Is that the way one can calculate the length and time corresponding to a mass?
Thanks

Makes sense, but I'd take a look at the equation you used to find the length. Do you really want to be using the reduced Planck constant (hbar) there, or simply the Planck constant (2*pi*hbar)? You can look up the de Broglie wavelength of an electron, and you'll see your value is a bit small.

That depends on the convention, right? For instance, in Peskin, the convention is to use hbar as the base unit (of action). I don't recall seeing anyone use just plane h as the base unit, but it is just a convention.

## 1. What is the relationship between energy and the mass of an electron?

The energy of an electron is directly proportional to its mass. This is described by Einstein's famous equation, E=mc^2, where E is energy, m is mass, and c is the speed of light.

## 2. How does time correspond to the mass of an electron?

Time is not directly related to the mass of an electron. However, the concept of time dilation, which is a result of the relationship between energy and mass, can affect the perceived time experienced by an electron or any other object with mass.

## 3. Can the length of an electron change based on its mass?

No, the length of an electron does not change based on its mass. An electron is considered a point particle, meaning it has no physical size or volume.

## 4. How does the mass of an electron affect its behavior?

The mass of an electron is a fundamental property that influences its behavior in many ways. For example, it affects how it interacts with other particles, how it moves in an electric or magnetic field, and its stability within an atom.

## 5. What is the significance of the mass of an electron in modern physics?

The mass of an electron is a crucial value in many equations and theories in modern physics. It helps explain the behavior of particles in the standard model and is also essential in understanding the behavior of atoms and molecules in chemistry and materials science.

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