Any real life demonstrations of radioactive decay? I'm skeptical about a lot of things in physics, but I have a great interest in it and I'm studying it in college next year. However I am very skeptical about some things. I find that for physics, it helps a lot to see a real life demonstration (video) of what's being explained. I understand the whole radioactive decay thing, but I have not been able to find a single video which shows an element decaying. Why is this? Does radioactive decay actually exist or is it a theory? Surely it cant be hard to put an element with a half life a a few days/weeks in front of a camera to show it's decay. If radioactive decay is occuring in an element, then how does the element ever actually form into a significant amount if it's constantly decaying? 
 A: Radioactive elements are formed naturally in any of several ways: in supernova explosions, from the radioactive decay of other elements, and by being struck by particles such as neutrons.
Stars release energy from nuclear fusion of elements starting from hydrogen, then helium, and continuing through progressively heavier elements. This can occur because there is a general progression from hydrogen up to about iron where heavier elements have less energy bound up in them (less actual mass) than the sum of the lighter elements which fused to create them. This release of energy allows the process to proceed. Most elements also exist in a sort of potential energy well which makes them stable... a lot of energy has to be put into a given nuclear reaction before it will occur, even though the reaction may release more energy than was input. This is why these processes only occur inside stars.
Beyond iron, the situation changes... heavier elements have more mass (and more energy) bound up in than the sum of the lighter elements which fused to create them. Some also exist in shallow potential wells. This is why they have a tendency to decay. It takes little energy to initiate a decay which releases energy. The reason the heavier/radioactive elements were created in the first place is that the conditions in a supernova involve extremely high energies... one direction some of that energy can go is into the creation of heavier atoms.
If it helps the above explanation, there is an analog of these nuclear processes in a common chemical process. Automobile engines tuned too lean and hot can form oxides of nitrogen - basically combining the oxygen and nitrogen from air. There is actually more energy bound up in these oxides than in the constituent molecules from which they formed. The point of this is that all processes be they nuclear or chemical are reversible given the right conditions.
A: Probably the best way to observe radioactive decay is to look for the radiation that is emitted. When a nucleus decays it moves from a higher energy state to a lower energy state. The difference in energy is radiated away. The radiation can take various forms such as a helium nucleus, a photon of light, an electron or even an anti-electron (called a positron). We can detect this using a device called a geiger counter. An example of this detecting radiation is shown in this video here: http://youtu.be/jDarcdMiIGs?t=1m43s
You can also "see" the radiation if the particles move faster than light would move through that medium. It's called Cherenkov radiation (https://en.wikipedia.org/wiki/Cherenkov_radiation) so we can see and detect radiation from radiative decays, but is the energy coming from a radioactive decay?
Well yes. Radon is a radioactive gas that isn't naturally found on Earth except that it is a decay product of uranium and thorium. Its most stable isotope, $^{222}\mathrm{Rn}$, has a half-life of 3.8 days, so the only way this stuff could be on Earth is if it was just created. And it is on Earth. It can be a big problem. Radon can build up in houses where the rock below contains traces of uranium and thorium, but this decays to radon. The radiation is stopped by the rock, so this isn't a problem, but the gas can leak into the house and decay in the rooms, exposing the inhabitants to sometimes high levels of radiation if there isn't enough ventilation.
So radon only lasts a few days before it decays so it shouldn't be on Earth, except that we do detect it and so the only explanation is that it was newly created, via radioactive decay.
A: Radioactive decay of an atom can not be seen directly by the human naked eye. Similar as why you can't see a single (stable) atom directly.
However if you are looking for a way of demonstrating it you might be able to use a bubble chamber. In this video they even talk briefly about being able to see it when a trail splits up in two.
