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Let's take a heavy atom (since velocity of electron is high in it) and project it with relativistic velocity. So the electron revolving around the nucleus in partial particle - wave character can have velocities in direction of motion of particle, opposite to it and in between.

So these will lead to fluctuations in the relativistic mass of the electron, it being higher on one side lower on the other. Will this mass difference lead to any changes in properties (permanent or temporary)?

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    $\begingroup$ Relativistic mass is an obsolete concept (although mathematically well-defined) that was dropped long ago. But first you should clarify how you're applying relativistic laws to such a system. "motion" of an electron inside an atom isn't well-defiined, and usually special relativity is only used for small corrections (hyperfine structure for example), unless you're going full-on quantum electrodynamics. $\endgroup$
    – Miyase
    Commented Dec 31, 2023 at 11:40
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    $\begingroup$ The problem here is you're considering electron as revolving around the nucleus, it should be considered as a quantum probability density around the nucleus. And if you are projecting an atom then the atom should be considered as a complete system and the velocity of the system should be same as velocity of every point inside the system. $\endgroup$
    – Aman pawar
    Commented Dec 31, 2023 at 13:28
  • $\begingroup$ @Miyase Thank you for clarifying, I am just a high school student, and ended up mixing various obsolete concepts and am not well versed in quantum physics at all. $\endgroup$
    – Le nerd
    Commented Dec 31, 2023 at 13:47
  • $\begingroup$ @Amanpawar Didn't even think of considering that, thanks a lot $\endgroup$
    – Le nerd
    Commented Dec 31, 2023 at 13:48

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The Dirac equation gives all the answers and fully agrees with experiment.

Relativistic mass is an obsolete concept.

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