Final answer:
Carbon has six protons and three natural isotopes: carbon-12 with six neutrons, carbon-13 with seven neutrons, and the radioactive carbon-14 with eight neutrons. The mass numbers vary according to the number of neutrons, with carbon-14 being a radioactive isotope used in radiocarbon dating while the other isotopes are stable.
Step-by-step explanation:
The atomic number of carbon is indeed six, meaning a carbon atom has six protons. Carbon has three naturally occurring isotopes: carbon-12, carbon-13, and carbon-14. All isotopes of carbon share the same atomic number of six, which indicates the number of protons, but they have different neutron counts and hence different mass numbers. Carbon-12 has six neutrons, while carbon-13 has seven, and carbon-14 has eight.
Carbon-12 and carbon-13 are both stable isotopes, because they do not change or decay over time. Conversely, carbon-14 is a radioactive isotope or radioisotope, which means it is unstable and can decay over time by emitting radiation, in this case resulting in the element nitrogen-14.
The different number of neutrons in each isotope affects the mass number but not the chemical properties of the element. Hence, carbon-12 and carbon-13 have mass numbers of 12 and 13, respectively, and carbon-14 has a mass number of 14. These differences in mass numbers are used significantly in various scientific applications, such as radiocarbon dating using the decay of carbon-14 to estimate the age of organic materials.