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Name: Richard
Status: student
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Question:
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?



Replies:
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 too.

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 uncertainty principle'.

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,

Burr Zimmerman


Richard,

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
Physics Instructor
Illinois Central College



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