What exactly makes the nucelus radioactive?

[m25]

I've heard that having equal number of proton and neutron makes an atom stable, but why exactly?
Also, the only radioactive atoms I've read about so far all have extra number of neutron, but do we also have a radioactive atom that has LESS number of neutron than in it's natural state, or is it very uncommon?

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[Cawolf]

http://chemwiki.ucdavis.edu/@api/deki/files/38743/2000px-Table_isotopes_en.svg.png?revision=1

This is a good image. It shows how there is an experimentally determined "stability line" (blue) where the nucleus does not tend to decay.

This is appreciably different than N=Z as you increase the atomic number. So heavier elements will tend to have more neutrons than protons while the ratio in light elements is closer to unity.

Light elements, such as He-3, would be useful for fusion. They would not be stable and tend to fuse to form a more energetically stable nucleus. You can note that they do show proton decay occurring in light elements when N<Z. So I guess the answer to question is yes.

 

[sazerac]

http://en.m.wikipedia.org/wiki/Weak_nuclear_force

That link will answer the question in the title of your post, but it is far far beyond the scope of the MCAT.