I analyze one atom of carbon in a rock and then one atom of carbon from one of my skin cells. Explain the differences I might see in these two carbon atoms.

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The two carbon atoms would be different. These different carbon isotopes are called isotopes. Isotopy is the existence of two or more atoms of the same element having the same atomic number but different mass number due to the difference in the number of neutrons in their various nuclei.

Carbon for example has 3 known isotopes which are:

¹²₆C ¹³₆C ¹⁴₆C

These isotopes have different places in nature where they can be found. Some can occur together naturally.

Isotopes have the same chemical properties because they share similar electronic configuration.