How many photons are emitted by accelerating electron?

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And what determines the wavelengths of the emitted photons? In jumping from one orbital to a lower one, how many photons does an electron generally emit? Is it just one, with a wavelength determined by the distance jumped between orbitals, or many?

In the case of an electron being accelerated in free space, does it emit a constant stream of increasing frequency photons, and how far must the electron travel in order to emit a photon?

Thank you.
 
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In transitioning from one orbital to another I *think* it just emits one photon of equal energy to the difference of the two energy levels. However, this does not prohibit an electron from dropping from one energy level to another, and then to one even lower provided it has free levels to drop to.

As for acceleration, that depends on the velocity of the electrons and the rate of acceleration. Many forms of X-Rays are produced by shooting electrons at a target and decelerating them. As for the number of photons emitted, I don't know.
 
Does anyone know the pertinent equations to figuring out the relationship between speed, time, and frequency of emitted photons to shed more light (pun unintended) on this?
 
Very interesting, thank you.
 
Insights auto threads is broken atm, so I'm manually creating these for new Insight articles. Towards the end of the first lecture for the Qiskit Global Summer School 2025, Foundations of Quantum Mechanics, Olivia Lanes (Global Lead, Content and Education IBM) stated... Source: https://www.physicsforums.com/insights/quantum-entanglement-is-a-kinematic-fact-not-a-dynamical-effect/ by @RUTA
If we release an electron around a positively charged sphere, the initial state of electron is a linear combination of Hydrogen-like states. According to quantum mechanics, evolution of time would not change this initial state because the potential is time independent. However, classically we expect the electron to collide with the sphere. So, it seems that the quantum and classics predict different behaviours!

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