Carbon atoms can be identified based on the # of which subatomic particles

protons and neutrons.

The nucleus is made up of 3 subatomic particles that are protons,neutrons and electrons.  

General notation of an element is

where, X is the Element, A is the Atomic Mass and Z is the Atomic Number

If we know the number of protons we can easily find out the atomic number of any element because Atomic Number = Number of protons in an element.

And in addition if we know the number of neutrons we can easily find out the atomic mass of an element because

Atomic Mass = (Number of protons) + (Number of neutrons)

If we get to know the atomic number and atomic mass, we can easily tell what element is it by looking from the periodic table.