Final answer:
The average atomic mass of the given sample of carbon atoms is approximately 12.84 amu, calculated by summing the products of the number of atoms and the atomic mass of each isotope and then dividing by the total number of atoms.
Step-by-step explanation:
To find the average atomic mass of a sample of carbon atoms with different isotopes, we consider the number of each type of atom and their respective atomic masses. Carbon-12, carbon-13, and carbon-14 have atomic masses of 12 amu, 13.003355 amu, and 14 amu, respectively. The formula to calculate the average atomic mass is:
average atomic mass = (mass of isotope 1 × number of atoms of isotope 1 + mass of isotope 2 × number of atoms of isotope 2 + mass of isotope 3 × number of atoms of isotope 3) / (total number of atoms)
Using the data given: 5 atoms of Carbon-12, 12 atoms of Carbon-13, and 2 atoms of Carbon-14,
average atomic mass = (12 amu × 5 + 13.003355 amu × 12 + 14 amu × 2) / (5 + 12 + 2) = (60 + 156.04026 + 28) / 19 = 244.04026 amu / 19 = 12.844228 amu.
Therefore, the average atomic mass for the given sample is approximately 12.844228 amu, which can be rounded to 12.84 amu.