Out of curiosity, did you use the classical or relativistic kinetic energy to calculate the trajectory?
If electrons actually 'orbited' a nucleus, then no atoms could ever form The electron would radiate away all its energy and fall into the nucleus in about 10 𝑡𝑟𝑖𝑙𝑙𝑖𝑜𝑛𝑡𝘩𝑠 of a secondpic.twitter.com/5JvjrhpAGl
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I used the classical limit, which let to this equation of motion (below) .. knowing that the relativistic corrections only decrease the capture time i just left it at thispic.twitter.com/ZrG0gPfxuz
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What’s the mechanism for energy loss?
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radiation!
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wait, why would it fall? planets can have stable orbits, why electrons can't?
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because the energy emitted by EM radiation is much more than that emitted by gravitational radiation (i.e. gravity is weak)
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why would the electron generate radiation while orbiting? also, if electrons don’t orbit the nucleus, but they also don’t ever collide with the nucleus, then what are they doing all the time?
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Because accelerating charged particles radiate. What they're actually doing is existing in a superposition of states that can be approximated to some extent (which breaks down fairly quickly) with a classical conception of orbits.
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Uhhhhh gimme some of that B r e m s s t r a h l u n g
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synchrotron
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