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The similarity among these "rays" is that they are all forms of radiation, and they are all produced by nuclear activity. An alpha ray is not a ray, but is a particle. It is a helium-4 nucleus, which is composed of two protons and two neutrons. The beta ray is not a ray, either. It is an electron, which is a beta minus particle, or it is a positron, a beta plus particle (which is the antimatter equivalent of an electron).

Either the alpha particle or the beta particle emerge from the nucleus of an atom during a particular type of radioactive decay event. Different particles are produced by different decay events, as you probably guessed. Gamma rays are also produced in nuclear events.

The gamma ray is the only "real" ray here. It is a high energy photon, which is electromagnetic radiation. The other two "rays" are forms of particulate radiation.

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