MadSci Network: Physics |
I will try to simplify the quantum mechancal answer for this. The electrons in an atom move about the nucleus in a cloudlike motion described by the electron's wave function. Quantum mechanics can be used to find the rms velocity (rms v is the square root of the average of v^2.) of any electron as the square root of the expectation value. That is v=sqrt{
}. For the ground state of the hydrogen atom, this is given by v=sqrt{2B/m}, where B is the binding energy. This QM answer is the same as the simple Bohr model would give, even though the Bohr model does not give the correct picture of how the electron moves about the nucleus. Numerically, for hydrogen, v=sqrt{2 X 13.6/511,000}c= 0.0073 c. The innermost and fastest electrons in heavier atoms will be given by Z times the Hydrogen result. The outer electrons will move more slowly as you go to the outer shells, and the slowest electrons in any atom will move at about the hydrogen speed. So that the rms electron velocity in uranium will vary from about v=0.007 c to about v= 0.7 c. The high velocity of the fastest electrons in heavy atoms would have to be corrected for relativity, but would still be about 0.7 c for uranium. If by "bound to other atoms" you mean covalent molecular binding, the calculation gets much more complicated. The fastest, innermost electrons would not be affected. The slower, outer electrons would have (I believe) only a slight change, probably a slight increase in their rms speed.
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