To determine the number of carbon atoms in the sample, you need to calculate the number of moles of carbon in the sample and then convert it to the number of atoms using Avogadro's number.
First, calculate the number of moles of carbon using the given mass of the sample. To do this, divide the mass of the sample by the average mass of a carbon atom.
Mass of the sample = 12.01 g
Average mass of a carbon atom = 1.994 x 10^23 g
Number of moles of carbon = Mass of the sample / Average mass of a carbon atom
Now, substitute the values into the equation:
Number of moles of carbon = 12.01 g / 1.994 x 10^23 g
Compute the result:
Number of moles of carbon = 0.006020 moles
Next, convert the number of moles to the number of atoms using Avogadro's number. Avogadro's number states that there are 6.022 x 10^23 atoms in one mole of substance.
Number of atoms = Number of moles of carbon x Avogadro's number
Now, substitute the values into the equation:
Number of atoms = 0.006020 moles x 6.022 x 10^23 atoms/mole
Compute the result:
Number of atoms = 3.623 x 10^21 atoms
So, there are approximately 3.62 x 10^21 carbon atoms in the given sample.