One easily ptoves by substituting known formula relations that lambda_C=(2pi/alpha)R_0, where alpha the fine structure constant.lanjarote said:
But wait: I think you mistaked the values
I have the for classical electron radious
Ro= e^2 /(mc^2)= 2.82E-13 cm.
and on the other hand, the compton wavelenght
LambdaC= h/mc= 24.3E-13 cm.
( m is the rest mass of the electron)
and the ratio is really LambdaC/Ro= 8.61 (dimensionless value)
The Compton Radius and Compton Wavelength are two different physical quantities that are related to the behavior of particles at the quantum level. The Compton Radius, also known as the classical electron radius, is the average distance from the center of an electron to its edge. On the other hand, the Compton Wavelength is the wavelength of a photon that would be scattered by an electron.
The Compton Radius is calculated as the ratio of the electron's charge squared to its mass multiplied by the speed of light squared. This is expressed as a mathematical formula: r_e = e^2/mc^2. The Compton Wavelength is calculated as the ratio of Planck's constant to the electron's mass multiplied by the speed of light. This can be represented as a formula: λ_c = h/mc.
The units of measurement for Compton Radius are meters (m) or centimeters (cm), depending on the system of measurement used. The units for Compton Wavelength are also meters (m) or centimeters (cm). These units represent the physical distance involved in the calculations and are based on the speed of light and the mass of the electron.
The Compton Radius and Compton Wavelength are important concepts in the field of quantum mechanics. They are used to describe the behavior of particles at the subatomic level and are essential for understanding phenomena such as electron scattering and the wavelength of photons. They also play a role in calculations involving the fine structure constant and the gravitational interaction between particles.
Yes, there is a relationship between Compton Radius and Compton Wavelength. In fact, the Compton Wavelength can be derived from the Compton Radius, as shown in the formula λ_c = h/mc. This relationship highlights the interdependence of these two quantities and their role in understanding the behavior of particles at the quantum level.