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What is the velocity of an electron within an atom?

This is a trick question. An electron within an atom doesn’t have a velocity. Despite what we are usually taught in grade school, it isn’t a particle zipping in an orbit around the nucleus. An electron is better described as having an orbital rather than an orbit. “Orbital” sounds something like an orbit, but it isn’t.

electron orbital
 Image of an electron orbital within a hydrogen atom. This is a computer-generated image. It was created by scientists in Amsterdam and appeared in the May 29, 2013 edition of the on-line science journal, New Scientist, [Image source: “Smile Hydrogen Atom, You’re on Quantum Camera.” The article reports on scientific work of Aneta Stodolna and others; FOM Institute AMOLF, Amsterdam, Netherlands]
orbital color key
Color Key for image of orbital. 

An analogy for an orbital is a cloud. The image to the left is a computer-generated reconstruction of an electron orbital, also called an “electron cloud.”


electron cloud around nucleus
Click for the animation. The electron can be visualized as an moving, energetic cloud around the nucleus. [Image source: http://toutestquantique.fr/en/]
The orbital has energy as illustrated in the animation to the right. But it doesn’t travel as a unit and so, doesn’t have velocity. Imagine it as a rain cloud that stores so much energy that lightning flashes out from time to time. But this is just a metaphor that doesn’t really do justice to the idea of an electron orbital. For a more precise understanding, see orbital.

Sometimes physicists calculate a velocity that corresponds to the amount of energy in the electron cloud. This approach is beyond my understanding. But I’ve read on-line in a couple of places that if the energy of an electron orbital in a hydrogen atom were translated into velocity, it would travel over 2,200 kilometers a second. At this speed, if the electron were to orbit, which it doesn’t, it would travel around the Earth in a little over 18 seconds. So, an electron orbital has a lot of energy, but it doesn’t have a velocity.