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No, the neutrons produced in nuclear reactors don't travel anywhere near the speed of light. Let's look at this a bit. In the "standard" fission reactor, fissile nuclear fuel is "started up" and the neutron chain reaction begins. Neutrons are produced during atomic fission events, and these neutrons are sometimes called "fission energy" or "prompt" or "fast" neutrons. They are the free neutrons that appear as the result of the fission event. And they're moving pretty darn quick when they're "blown out" of the fissioning nucleus. But they're not moving anywhere near the speed of light. The Boltzman distribution (a fancy way of speaking about the range of energies at which the fast neutrons appear), has a strong peak at close to 2 MeV (20 TJ/kg). That translates into a speed of 28,000 km/s. The speed of light is some 299,792 km/s as we've defined it, and that puts the speed of those fast neutrons at roughly 10% the speed of light.

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