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An electron spins about it's own axis. So it has rotational accln. Thus, according to Maxwell's Electromagnetic Theory , Rotational Kinetic energy must be released. Thus, at some pt. of time , shouldn't the energy of an electron become 0 & then shouldn't the electron move out of the atom, eventually leading to the atom only having the nucleus .

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    $\begingroup$ The electron isn't spinning on it's own axis $\endgroup$ – John Rennie May 25 '16 at 6:10
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    $\begingroup$ Why aren't you concerned with electron's "rotation" around the nucleus in the first place? (The explanation is pretty much the same: there is no actual rotation.) But wait, there is more to it: a free electron has spin as well! Had it lose energy through some mechanism, what would eventually become of it? $\endgroup$ – Ivan Neretin May 25 '16 at 7:43
  • $\begingroup$ hey @IvanNeretin , I do know about the rotation of electrons around the nucleus(in fact it was a defect of Bohr's Theory). My question's pretty similar(though it's about rotation of electrons about it's own axis). Hope u get my question. $\endgroup$ – Tamoghna Haldar May 28 '16 at 7:06
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You are confusing macroscopic spin with the spin angular momentum of electron here. Electron is a point entity and does not posses a macroscopic spin (i.e. it does not spin on its axis). It does have angular momentum which is expressed as 'spin angular momentum' which is of-course quantized.

This link by John Rennie will be useful for understanding : The electron isn't spinning on it's own axis

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