Question

What conclusions can be drawn about the existence of carbon-12, carbon-13, and carbon-14?

Answer 1

These are isotopes of carbon and they all contain 6 protons and 6 electrons but each contains a difference number of neutrons - 6, 7, and 8 respectively.

^ This is the answer because an isotope changes the atomic mass, NOT atomic number. That means that the neutrons are changed, not the protons. 

Answer 2

Answer: These are isotopes of carbon and they all contain 6 protons and 6 electrons but each contains a difference number of neutrons - 6, 7, and 8 respectively.

Explanation: Isotopes of an element have similar number of protons but different number of neutrons.

General representation of an element is given as: $_Z^A\textrm{X}$ where,

Z represents Atomic number  (for neutral atom) = number of protons= no of electrons

A represents Mass number  = number of protons + number of neutrons

X represents the symbol of an element

Thus  $_6^{12}\textrm{C}$ ,   $_6^{13}\textrm{C}$ and  $_6^{14}\textrm{X}$ all contain same number of protons i.e 6 but contain (12-6) =6, (13-6)=7 and (14-6)=8 neutrons respectively.