Exercise 3 solution

Your friend is not right. Both are carbon.

What defines an element is the number of protons (the atomic number). The Atom and Atomic number articles say the elements are distinguished by their number of protons. Carbon-12 and carbon-14 both have 6 protons, so both are carbon.

What differs:
  - Neutrons: carbon-12 has 12 - 6 = 6; carbon-14 has 14 - 6 = 8 (two more, as your friend said).
  - Mass number (12 against 14) and so atomic mass.
  - Physical properties; the Isotope article also notes that carbon-14 is radioactive.

What does not differ:
  - Number of protons (6) and, in an uncharged atom, number of electrons (6).
  - Chemical properties, which are "virtually the same" for all isotopes of an element (Isotope article).

Atoms with the same proton count but different neutron counts are, by definition, isotopes of the same element. Only changing the number of protons would give a different element.

The neutron counts were checked with Python.