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Why do the electrons revolve around the nucleus in circular motion not like the earth which revolves around the sun in an eliptical motion?

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What makes you think they do? At that scale, position and velocity are more probability functions than a defined path and speed. –  Olin Lathrop Jan 7 at 16:50
    
maybe you could understand this wiki entry on the orbitals en.wikipedia.org/wiki/Atomic_orbital –  anna v Jan 7 at 17:23
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2 Answers

They don't. That is a simplistic model that is frequently taught at lower levels because some of the math coincidentally works out and it gives you a vague (but ultimately false) idea of how the atom works.

In reality, there are "stable orbits" that describe the probability of finding the electron there, but it is not just going around in a circle.

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It is not taught just because it happens to work out, it is also a stage of the evolution of understanding in the early 20th century. I mean, Bohr wrote a seminal paper in which circular orbits were one of the underlying assumptions. Which doesn't make it any less likely to leave casual students of physics with the wrong idea. –  dmckee Jan 8 at 0:30
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Welcome to Physics.SE. More importantly, welcome to Quantum Mechanics!

The circular orbit electron model which you are talking about is called the planetary model/Rutherford model of the atom which was proposed by E. Rutherford in the early 20th century. But this model has an inconsistency! The electromagnetic theory of Maxwell predicts that accelerating charges lose energy, hence, leading the rutherford electron to die out! Then Niels Bohr came to the rescue and said that the electrons around the nucleus are special and instead revolve in fixed in orbits with fixed energies. He said this and also that the angular momenta of the electrons was "quantized" i.e, they come only in fixed multiples of some constant, like currency.

This developed into a much more advanced theory in which the path of revolution went from circular to elliptical to probability distributions. These are nothing but the orbitals of an atom, if you're in high school you might have heard of them being called as "1s 2s 2p...etc"

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