Electron Orbital Velocity and Mass
If an electron's orbital speed approaches the speed of
light, what happens to its mass? Does it become significantly
greater than 9.11 X 10 -31kg?
It sounds like there are some misconceptions embedded in this question that
I would like to clarify. Unfortunately, I cannot answer your question as it
is written, but hopefully the information below will help you re-frame the
question in your mind. I suggest some additional reading that might help
First, an electron orbital does not have a 'speed' in the sense of a moon
orbiting a planet. The electron orbital describes the probability of finding
an electron at a given place. If you think of an orbital as a cloud, you can
think of the more 'opaque' areas of the cloud as being more probable to
contain the electron, and the more 'transparent' areas of the cloud as less
likely. I would also suggest you think of the cloud as not moving relative
to a point of reference (the atom) -- or rather, that movement is
representative of chemical changes in the molecule rather than other motion.
It is also misleading to think of a 'solid' electron darting from point to
point within the orbital. It is more accurate to think of the electron as
'smeared' all across the orbital all at the same time (with "more" of the
electron where it is more likely to be according to the orbital shape and
density). Only when we make certain kinds of measurements does the electron
appear to be in one place.
If you want to know more about electron orbitals and density, I would
web-search 'orbital' or 'orbital density' to start.
There is also a concept known as 'uncertainty' which essentially means we
cannot know everything about the electron (especially relating to velocity
and position). The more accurately we know its position, the less accurately
we can know its velocity, and vice versa. The problem is for a single
particle, that makes a big difference in terms of measuring the mass of a
moving electron. To learn more about this, read about 'Heisenberg's
The above concepts relate to quantum physics. There is also a branch of
physics known as relativity. Relativity is a concept developed and observed
in very large objects (stars, galaxies, etc.). Gravity plays a big role in
relativity. Quantum mechanics are observed in very small objects (individual
particles and waves -- electrons, photons, etc.). Science has not yet
unraveled a quantum description of gravity yet. As of right now, there is
still a lot of work being done trying to unify the two branches.
Relativity is the branch of physics that describes how objects' properties
(and their perception of time) change as their velocities change. You ask
about the mass of an electron changing with velocity, which is a
relativistic concept (not a quantum concept). The concept of 'velocity' is
questionable for a single particle as I explained above. Electrons
(especially those in orbitals) are not the theoretically perfect spheres
that would make relativistic calculations easy to apply to them. The short
answer is that it is not quite right to think of an electron as 'moving
really fast around a nucleus' and therefore having 'greater mass because
it is moving so fast'.
Electrons do have an 'effective' mass in various systems, and part of that
is their velocity. The question I cannot answer (I do not know) is to what
degree various factors influence the effective mass of electrons in
orbitals. The presence of various energy states, excited states, magnetic
fields, system velocity, and many other factors influence the effective mass
of an electron. Is part of that due to an average velocity described by the
orbital? Possibly, but this is the limit of my knowledge.
I do not pretend to be an expert on relativity or quantum mechanics (or on
teaching them) so I will stop here -- but the concept of mass as it relates
to single particles will help to learn more about this. I recommend you read
about special relativity, relativistic mass, and gamma factor (and reading
these will give you ideas for further reading if you like).
I hope this helps,
Here you reach one of the problems that inspired string theory to be
developed. Quantum physics (electron in an atom) and relativity
(changing mass) do not agree with each other. An electron's orbital
speed is not a clearly defined quantity. You can calculate the AVERAGE
speed, but not the electron's speed at any particular moment. While
orbiting in an atom, an electron behaves more as a wave than as a
particle. Electrons do not orbit in circles. They fill
three-dimensional distributions, rather than following a specific path.
As an example, consider an electron in an s-orbit, i.e. zero angular
momentum. The electron has no angular momentum and yet it does exist in
a shell around the nucleus. Based on energy level, speed is large.
Based on angular momentum, speed is zero.
Dr. Ken Mellendorf
Illinois Central College
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Update: June 2012