Some days ago, I was reading a very simple text about photoelectric phenomenon (at high school level) that this question came to mind. How do electrons move (for example during their translation from cathode to anode in photoelectric phenomenon)? Is motion of an electron pure translation or electron rotates about its axis (if it is a tiny sphere) and translates simultaneously (like the earth motion)? In other words, what is an electron kinetic energy? Is it equal to $\large{\frac 12}m_ev_e^2$ or $\large{\frac 12}m_ev_e^2+\large{\frac 12}I\omega ^2$?

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    $\begingroup$ As far as experiment can ascertain, electrons are just points - they don't have a size and therefore lack a classical angular momentum. Related: Why can't I just think the spin as rotating? $\endgroup$ – lemon May 24 '16 at 13:19
  • $\begingroup$ @lemon Thank you because of your attention. If electrons are just points, then how they have mass? $\endgroup$ – lucas May 24 '16 at 13:21
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    $\begingroup$ An electron is always associated with a spin state. Also the spin does not represent a degree of freedom, even though it is a characteristic of an electron. So there is no motion associated with a spin. Hence there is no rotational kinetic energy of an electron. Spin angular momentum does not cause the electron motion. So the electron motion is purely translational $\endgroup$ – UKH May 24 '16 at 13:25
  • $\begingroup$ Electrons aren't point particles. They aren't little balls. No easy picture like this correctly describes how electrons behave. This is why quantum mechanics was invented. QM is counter intuitive and appears to be wrong when people used to the everyday world think about it. But it does describe how electrons behave. Electrons have no size or shape, but they do have mass and spin. You can't say exactly where they are or how fast they are going. $\endgroup$ – mmesser314 May 24 '16 at 13:29

The electron energy (the portion that changes at least) will be mainly due to kinetic energy (translational) and potential energy due to the potential difference between the cathode and the anode.

The electron does have a "spin", but this spin isn't like that of a spinning sphere. The reason for the name spin is simply that the electron spin describes the angular momentum of the electron, similar to how a rotating sphere has a angular momentum. In fact all electrons have the same spin value, and can't be "spun" faster or slower.

In this case, you could think of the electron as a wave. And the frequency of the wave would change as the speed changes. The frequency is related to the momentum, which is related to kinetic energy and more.

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