Prefactor of classical electron radius

In summary, the classical electron radius is derived by equating the energy of the electric field with mec2, assuming a charge distribution. The prefactors (3/5 or 1/2) for constant charge density and surface density are often ignored in order of magnitude calculations, while the factor 4 in the denominator is kept due to its relation to other physical constants.
  • #1
greypilgrim
533
36
Hi,

Assuming the electron is a sphere of finite extent, the classical electron radius is derived by equating the energy of the electric field with mec2. For the computation of the field energy, we have to assume a charge distribution. Both constant charge density and constant surface density lead to prefactors (3/5 or 1/2) which are somehow just ignored.

Why? If we are only interested in the order of magnitude, why drop these prefactors but keep 1/4?
 
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  • #2
I think it's just for "vague ballpark" calculation, yeah, since the prefactor depends on rather arbitrary assumptions (charges are on surface, or equally distributed). Regarding the factor 4 in the denominator, that one is likely left in there because it comes from the other physical constants, not the geometrical assumptions.
 

Related to Prefactor of classical electron radius

What is the prefactor of classical electron radius?

The prefactor of classical electron radius is a constant value used in the calculation of the classical electron radius, which is the theoretical size of an electron based on its mass and charge. It is denoted by the symbol alpha (α) and has a value of approximately 7.297 x 10^-3.

Why is the prefactor of classical electron radius important?

The prefactor of classical electron radius is important because it helps us understand the size and behavior of electrons, which are fundamental particles in the field of physics. It also plays a crucial role in various equations and theories, such as the Bohr model of the atom and quantum electrodynamics.

How is the prefactor of classical electron radius calculated?

The prefactor of classical electron radius is calculated by taking the square root of the fine-structure constant (α) which is equal to the square of the electron charge (e) divided by the product of the speed of light (c) and the Planck constant (h). The resulting value is approximately 0.0072973525664.

What does the prefactor of classical electron radius tell us about the electron?

The prefactor of classical electron radius tells us about the size and charge of the electron. It is a fundamental constant that describes the strength of the electromagnetic interaction between particles and helps us understand the behavior of electrons in different physical systems.

Is the value of the prefactor of classical electron radius exact?

No, the value of the prefactor of classical electron radius is not exact. It is an experimentally determined value that may vary slightly depending on the measurement method used. However, it is a very precise value and is considered a fundamental constant in physics.

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