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I read here that the orbital speed of an electron around a proton can be calculated as:

$$\frac{m_ev^2}{r} = F_G+F_E$$

where $F_E$ is the proton-electron electromagnetic force, $F_G$ is the proton-electron gravitational force, $m_e$ is the electron mass, $r$ is the orbital radius (radius of hydrogen atom) and $v$ is the orbital speed. Is this a correct way to calculate the orbital speed of an electron?

Kyle Oman
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Bibek Dhakal
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    A better way would be to compute $<\psi|p^2|\psi>$ and figure out rms velocity from there. – Jahan Claes Aug 26 '15 at 15:38
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    It is also better not to think of the electron being in an orbit at all - as @JahanClaes indirectly points out, it is a wavefunction around the nucleus. – Jon Custer Aug 26 '15 at 15:41
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    An bound electron doesn't have a velocity because it is not in "orbit". It's a quantum object and it forms a bound state identified with an "orbital" and those words do not mean the same thing. The Rutherford/Bohr picture may be intuitively appealing but it is more wrong than right. What @JahanClaes suggests is at least defined, but you shouldn't think of that as giving an "orbital velocity". – dmckee --- ex-moderator kitten Aug 26 '15 at 15:41
  • possible duplicate of Why don't electrons crash into the nuclei they "orbit"? – Jon Custer Aug 26 '15 at 15:56
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    Welcome to Physics.SE! Rather than giving only a link in your question, try to at least summarize the important information you are linking, in case for instance the link ever dies. I've edited things in here as an example (notice also how math can be nicely formatted - click edit to see how this was done). – Kyle Oman Aug 26 '15 at 16:54

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The idea of electrons orbiting the nuclus is called the Bohr model and has now been replaced with a quantum model. Electrons exhibit wave-particle duality, which means they sometime act like a wave and sometimes like a particle. They don't actually orbit the nucleus but have areas around it where you are more likely to find them called orbitals.

The equation is wrong even if electons did orbit. It includes a centrifugal force which does not exist, a centrifugal force is just a centripetal force from a different perspective and the centripetal force in this case is the electrostatic force plus weight (Force due to gravity). Also, orbits are elliptical not circular.

Altra
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