91Ó°ÊÓ

A moving electron and a third body (atom or nucleus) must be present.

Energy-momentum relation, or relativistic dispersion relation, relativistic equation related to the amount of energy (also called relativistic energy) and constant weight (also called resting weight) and intensity. It is the extension of the equilibrium of the major forces in the body or systems with non-zero pressure forces. It can be written as the following numbers:

${\mathrm{E}}^2={\left(\mathrm{pc}\right)}^2+{\left({\mathrm{mc}}^2\right)}^2$ ….. (1)

Here, E is the energy, p is the momentum, c is the speed of light, and m is the mass.

Using the energy-momentum relation of a four-vector body, predict whether the electron moving with the given energy can spontaneously change into an x-ray photon. It will also justify the reason for having a third body in the system.

Suppose an electron with total energy E and momentum p spontaneously changes into a photon. If energy is conserved, the energy of the photon is E and its momentum has magnitude E/c

Now using equation (1) and further writing it, the energy and momemtum relation as follow.

$\mathrm{pc}=\sqrt{{\mathrm{E}}^2-{\left({\mathrm{mc}}^2\right)}^2}$

Since, the electron has non-zero mass; thus, E/c and p cannot have the same value considering the above relation.

Hence, the momemtum cannot be conserved. A third particle must participate in the interaction, primarily to conserve momemtum and also does it carry off some energy.

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