This is an introduction to nuclear chemistry, the chemistry of different nuclear reactions and radioactive materials.
As you probably know, the atom is made of electrons, neutrons and protons. The nucleons are made of subatomic particles. Atoms were first theorized by the Greeks in 350 B.C. They thought that everything had its own type of atoms e.g. humans have human atoms and dogs have dog atoms. This model existed until the 1800's. Then, John Dalton, an English chemist said that atoms can combine in specific ratios to create compounds. Then in 1897 Joseph John Thompson discovered the electron and said that there was an equal distribution of positive and negative charges within the atom. In 1911, Ernest Rutherford performed his gold foil experiments, and discovered that the atom had a positively charged center, and had electrons moving around it. In 1913, Neil Bohr created the planetary model where the electrons would orbit the positively charged center of the atom like the planets orbit the Sun.
The modern atomic theory is that the electrons do not follow a specific path around the nucleus and that you can never know the exact location of an electron in an atom, but only have a probability of finding them.
Isotopes are when the number of neutrons and protons in an atom are different. Also, having a large difference between the number of protons and neutrons can cause an elements isotope to become radioactive, even if the original element wasn't (e.g. in the case of Carbon-14). Radioactive substances produce radiation in the form of particles (such as alpha particles and beta particles) and electromagnetic waves (e.g. Gamma rays). The number of neutrons and protons added together in an isotope determine its mass number.
I am doing this part of nuclear chemistry early in the article since there is a lot of confusion about what radiation is. It is simply the process of emitting energy in the form of particles or waves. It can be dangerous, but most types are not. There are two types of radiation, ionizing and non-ionizing. Ionizing radiation has the power to remove electrons from atoms, creating ions (we will learn about that later). That is why they are so dangerous, and can cause cancer (but they can be used in good ways: to kill cancer cells, generate power, sterilize substances etc.). The four main types being alpha, beta, x-ray and gamma. An alpha particle is a nucleus of helium with a mass number of 4.  That means that there are two neutrons and two protons in the particle. A beta particle is simply an electron, and gamma and X-rays are pure energy, with no mass or charge. X-rays are used to diagnose medical problems, such as a broken arm or leg. Even though they have the ability to mutate cells and DNA as well as cause cancer.  They are extremely useful in the medical field. Gamma rays are often used to kill cancer cells. Because cancer cells grow so fast, gamma rays are much more effective at killing them than normal, healthy cells. Non-ionizing radiation does not have the ability to change atoms into ions, thus not being able to cause cancer.
Here is a diagram of the electromagnetic spectrum:
What are Ions? Well they are simply atoms or molecules that have a charge, where they have less or more electrons than they should.  There are two types of ions, anions and cations. Anions have more electrons than protons, giving them a negative charge  and cations have more protons than electrons, giving them a positive charge. If an ion has unpaired electrons in them, they become very reactive.  An example of an ion is sodium, which reacts violently with water. When combined with chlorine it creates table salt. In fact it is so reactive that it has to be stored in a hydrocarbon (e.g. gasoline, kerosene etc.) otherwise it will explode. .
Sometimes elements are unstable, and they decay into more stable elements. Some do this slowly, in a matter of thousand, millions or even billions of years, while others do it quickly, sometimes in a matter of milliseconds. Any radioactive isotope has a half life, that is how long it will take half of a certain amount of radioactive material to decay into a different isotope. For instance, Uranium-234 has a half life of 245,000 years, so after 245,000 years a 1-gram sample of Uranium-234 would have only 1/2 gram of Uranium-234 in it. For this isotope, every 245,000 the amount of Uranium-243 in a sample is cut in half. So after 490,000 years, 1/4 of a grams of Uranium-234 will remain in the sample. Different isotopes of different elements generally have different half-lifes. For instance, Polonium-214 has a half life of 163 microseconds (a microsecond is one-millionth of a second).  When this process is started artificially, it is called transmutation. 
This is an example of an artificial transmutation, this one being called a fission reaction:
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- "Isotopes." Web. 5 Dec 2009. <http://www.colorado.edu/physics/2000/isotopes/index.html>.
- "Non-Ionizing Radiation Information | Radiation Safety | Safety Programs | EHRS." Penn: University of Pennsylvania. October 27, 2009. University of Pennsylvania, Web. 5 Dec 2009. <http://www.ehrs.upenn.edu/programs/radiation/nonionizing_faq.html>.
- "WordNet Search - 3.0." Princeton University, Web. 5 Dec 2009. <http://wordnetweb.princeton.edu/perl/webwn?s=ion>.