For example, a Hydrogen atom, has 1 proton, so it's atomic number is one. No matter how many neutrons it has, as long as the number of protons does not change, the atomic number is still one, and the element is still Hydrogen. I say this because if we add a proton to the nucleus, then the element is no longer Hydrogen, it is now Helium. To see what atomic numbers are what elements, just look at the periodic table of elements. If you cant see it, just click to enlarge.
We know by looking at the periodic table that Helium's atomic number is 2, so it has only 2 protons. But, it can have a different number of neutrons. As you can see, under the symbol for Helium, it says 4.0026. This is Helium's atomic mass, measured in amu (atomic mass units). A proton and a neutron each approximately weigh one amu, so 2 of those amu come from the 2 protons in the Helium atom's nucleus, and the other 2 amu come from the two neutrons.
This doesn't mean that every single Helium atom has 2 protons and 2 neutrons. This is just the majority of naturally occurring Helium. So to find out how many neutrons are in an atom of a single element, round the atomic mass to the nearest amu, and then subtract the atomic number from it. Let's do an example.
I'll use an element we all know, Oxygen. The atomic mass of Oxygen is 15.999. So then we round this to 16. That means most naturally occurring Oxygen atoms have 16 nucleons(remember that word?). The atomic number of Oxygen is 8, which means it has 8 protons. Since there are only two types of nucleons, protons and neutrons, there can only be neutrons left in the nucleus. 16 nucleons - 8 protons = 8 neutrons. So most Oxygen atoms have 8 protons and 8 neutrons, giving it an atomic mass of 16.
This is an isotope of Oxygen. An isotope of an element, is an atom with the same number of protons, but a different number of neutrons. For example Hydrogen has different isotopes. Hydrogen usually has only one nucleon, a proton, and no neutrons. But sometimes it can have 2 or 3 neutrons. To write down the isotope of an atom, we would write down the number of nucleons on the top left corner of the symbol of the element.
I unfortunately can't type that on this blog, so i will just do it in a way that is different but still works. Hydrogen with one proton, and no neutrons, would only have one nucleon, the proton, so we would write a little 1 in the top left corner of the H to represent hydrogen. Instead I will write it like this; H-1.
If the Hydrogen atom had a proton and a neutron, it would be written like this H-2, because there are only two nucleons. H-1 and H-2 are different isotopes of Hydrogen.
What happens if we add more neutrons to the nucleus of the hydrogen atom? If I added 5 neutrons to a Hydrogen atom creating the isotope H-6 (5 neutrons + 1 proton), it would be "destroyed" almost instantly. Why? Because it is unstable.
'But why is it unstable?', you might ask. Well can you hold on for one second I'm trying to explain, jeez what's your problem? It's unstable, because there are two many neutrons per proton, and the force that keeps them together, the strong nuclear force, cannot hold on to them, so they some neutrons are released, to make it stable again. This is known as nuclear decay, and this is what causes radiation. The release of particles from unstable atoms.
But neutrons are not the only thing that can be released, electrons, gamma rays, protons, and more. It all depends on the situation. But that doesn't mean if you take away all the neutrons from an atomic isotope will make it stable. Just the opposite, if we take all the neutrons out of an Oxygen atom, and there are only 8 protons in the nucleus, the positive charges are not balanced, so protons are released. Remember how I said that protons have a positive charge? Well, opposites attract, and... not opposites repel. So protons are released. But not only particles are released, but also energy. In fact that's why atoms decay in the first place because they have too much energy.
The half life of an isotope is half the time it takes for a certain amount to decay half way. For example Carbon's half life is about 5,730 years. So if we have a kilogram of carbon and leave it for 5,730 years, there will only be .5 kilograms, the Carbon would've decayed into Nitrogen. And if we leave it for another 5,730 years, it will be .25 kilograms of carbon, and etc. But that doesn't mean that after 5,730 years all the atoms decay at once. They decay over time, and the half life is the average amount of time for half of them to decay. If a radioactive isotope of an atom has a half live of 3 hours, and we have 1,000 grams of that atom, in 3 hours we would have 500 and this process would continue until all the atoms are decayed. After ten half-lives, only .1 percent of the original radioactive atoms remain. This is true for any radioactive material.
Now that I've taken all this time to explain all this physics and science, your probably bored or just plain tired. Now I'm gonna get to the good stuff. More physics.