Re: Does element mass = # of electron + neucleons??

Jeckyl wrote:
Yes .. but does an electron actually 'move'.

As is often the case, you need to be more precise, here in defining what you mean by "move". For instance, one might imagine that the electron in an hydrogen atom "moves" in the following sense: If one measures its position at time t0, and again at time t1, being careful to not disturb the atom as a whole, one obtains different positions (except possibly for rare cases when it happened to come back). This fails because to measure the position accurately enough to localize it inside the atomic size requires so much energy that the atom is ionized and cannot remain an atom.

Here's an attempt to define "move" classically: as the electron is both charged and bound in the atom, if the electron "moves" then it must be accelerated and thus radiate electromagnetic waves. None are observed, so the electron does not "move".

For further discussion I must use nonrelativistic quantum mechanics, using the ground state of the electron in the hydrogen atom. I'll assume the nucleus of the atom remains fixed in space (unrealistic to be sure, but it greatly simplifies the discussion and is faithful to what was asked).

Perhaps this meaning will do: the electron "moves" if the expectation value of its position changes with time. For this meaning the electron does not "move".

Perhaps this meaning will do: the electron "moves" if it has nonzero expectation value of 3-momentum in some direction. For this meaning the electron does not "move" (contrary to what others have said -- simple proof: the ground state is spherically symmetric, so there is no direction in which the expectation value of the 3-momentum could point, hence it must be zero).

Perhaps this meaning will do: the electron "moves" if it has nonzero expectation value of orbital angular momentum. For this meaning the electron would not "move" if it is any S state, but would move if it is in any other bound state. As the ground state is S, the electron does not "move".

.... I'm sure that other possible meanings of "move" could be found, but I think this gives the basic idea: I know of no meaning of "move" that applies to the electron of a hydrogen atom (in its ground state, relative to the nucleus). Note also that had you asked instead "does the electron spin?", the answer would be unambiguously in the affirmative. So I leave it to you to figure out how an electron can "spin" without "moving"....


Tom Roberts
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