How many neutrons can you add to an atom without it getting unbalanced?
The number of neutrons that an atom can carry is dependent on what it is. Some will become unstable with only one extra or one less neutron while others can hold or lose many extra. It varies from atom to atom and also within atoms.
Take a look at a Periodic Table. The atomic number is the number of protons in that atom. If you change the number of protons the atom becomes something else. The atomic weight is a little harder to figure. The atomic weight minus the atomic number equals the number of neutrons. You can mess around quite a bit with the number of neutrons and still have almost the same atom.
You might notice that while we assign whole number masses to subatomic parts, the atomic weights are not listed as whole numbers. Most elements exist as different isotopes, meaning they have different numbers of neutrons. The atomic weights listed in the periodic table are the weighted averages of the atomic weights of the various isotopes, weighted according to their distribution in nature. What that means is when they find an element, perhaps 20% is found of one isotope, 78% of another and 2% of a third. The Periodic table will list the atomic weight as being what that mix weighed instead of what a single element weighed. In the places where a whole number is given, it usually means that there is no stable isotope form of that atom. So you can see from looking at the periodic table that the number of neutrons does routinely vary quite a bit within a given atom.
If you want your answer for a particular element, look at the periodic table link above. Click on the element you are curious about and click on the isotope data. That will show all the different isotopes of that element. It also lists the half-life of that isotope so you can get an idea how stable that isotope is.
Brian Kross, Chief Detector Engineer (Other answers by Brian Kross)