The nucleus of an atom is made up of protons and neutrons. So if there are many protons inside nucleus even though there are neutrons why don't this protons may repel away breaking nucleus apart?
The answer I get is "it is because of the nuclear force (which is the strongest force)". When I asked this question to my chemistry teacher he was like you just destroyed chemistry..
I think this is the right place to ask it.
As you say, it is because of the nuclear force. The charges do repel each other, but not strongly enough to overcome this other, stronger force. However, this is why in nature the neutrons in a substance tend to outnumber the protons--the neutrons can provide additional nuclear force without adding to the electrical repulsion. Having only protons isn't stable--which is why helium can have mass number 3 or 4 but not 2.
Your teacher referred to "breaking chemistry" because in usual chemistry the atoms themselves are unchanged, but rearranged into different molecules. You might be interested in the field of nuclear chemistry, which studies how chemistry is modified by nuclear properties.
