There are 0.538 moles of ¹³C atoms in the given 7.00 g sample.
This is a simple mole conversion problem. It requires the molar mass, or the mass of one mole of a substance, of carbon - 13, an isotope of carbon. An isotope is like a different version of a specific atom. In this case, carbon - 13 is a version of a carbon atom that has one more neutron than the normal carbon atom. It is a little heavier than the normal carbon atom because of its extra neutron.
To convert from grams of sample to moles of sample, the general equation is:
[tex]moles \ of \ sample = \frac{given \ mass}{molar \ mass}[/tex]
To convert 7.00 g of ¹³C, the equation is:
[tex]mole \ of \ ^{13}C \ = \frac{7.00 \ g}{13.00 \ \frac{g}{mol}} \\\boxed {mole \ of \ ^{13}C \ = 0.53846 \ mol}[/tex]
Since there is only 3 significant figures in the given, the final answer must also have 3 significant figures. Therefore,
[tex]\boxed {\boxed {mole \ of \ ^{13}C \ = 0.538 \ mol \ or \ 5.38 \times 10^{-1} \ mol}}[/tex]
This answer is logical since one mole of ¹³C will have a mass of 13.00 g. The given sample (7.00 g) is less than 13.00 g so the mole equivalent of that should be less than one mole.
