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An isolated electron cannot emit a photon on its own as this process would violate energy and momentum conservation. An electron has constant internal energy equal to m_ec², where m_eis the rest mass of an electron and cis the velocity of light.

If an electron emits a photon, its internal must drop increasing the kinetic energy of the photon. But, this cannot happen as the electron's internal energy is always a constant and cannot drop.

Also, from the conservation of momentum, the final momentum of the electron and photon must be equal to the initial momentum of the electron. Considering the rest frame of the electron, the initial and final momentum of the electron is zero. This implies that the momentum of the photon after emission must be zero for momentum conservation. Again, this violates the known fact that photons always carry momentum and can never be zero.