Imagine a brick wall. Bricks are held together by mortar, so they form a single object. That’s an atom.
Now, take a brick wall that is much too big/high to hold together. Too many bricks sitting on not enough mortar; it is swaying in the wind and can come down any minute. This is an atom of a radioactive material.
Then, that wall finally falls down at a random moment. Bricks and mortar dust go flying everywhere. This atom just has undergone radioactive decay and everything that goes flying is what we call radioactivity.
The source of the energy was the energy that was used to put the wall up. The flying bricks, brick parts, dust, pieces of mortar, etc. are the different kinds of radiation. FivedozenWhales has given a very nice list of the types.
The bricks are alpha; they don’t fly very far or fast, can easily be caught with simple netting, but if they hit you, they really hurt. Pieces of bricks are neutrons; they go through nets, are quite fast, and when they hit another unstable wall, they have enough energy to bring it down. The dust is EM; it goes everywhere, nets do nothing against them, and while not the most energetic, you don’t want to get a lungful (or eyeful) of dust.
And yes, you can call something “glowing” when it emits EM radiation, but we usually restrict that word to mean “emitting visible light”. You wouldn’t describe a radio antenna as glowing because it emits radiation radio waves. Radio is just as invisible as X-rays and gamma to us; in fact, we can only see a very tiny part of the EM spectrum. For secondary effects, where radiation causes something to glow, see MercurianAspirations’s answer.
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