Final answer:
Carbon-14 is made up mostly of protons and neutrons, with six protons and eight neutrons. Carbon-12 contains six neutrons, and carbon-13 contains seven neutrons, based on their mass numbers of 12 and 13, minus the atomic number of carbon, which is six.
Step-by-step explanation:
Most of the mass of a carbon-14 atom is made up by two types of particles: protons and neutrons. The mass number represents the sum of these particles within the atom's nucleus. For carbon-14, the mass number is 14, which comprises six protons and eight neutrons, as the atomic number of carbon is always six. The other two stable isotopes of carbon are carbon-12 and carbon-13.
Given the mass number and atomic number for carbon-13 being 13 and 6, respectively, there are seven neutrons in a carbon-13 atom (mass number minus atomic number). Correspondingly, for carbon-12, which has a mass number of 12 and an atomic number of 6, there are six neutrons.
Options c and a from the reference information correctly state the atomic numbers for carbon-12 and carbon-13, as well as providing the correct number of neutrons for each. Therefore, carbon-12 has six neutrons, and carbon-13 has seven neutrons.