The atoms in a sample of carbon must contain nuclei with the same number of

Protons

Explanation:

All the atoms in the carbon sample will contain the same atomic number, represented by Z.

Also, the nucleus of an atom consists of protons and neutron and for the atomic number to be same, the number of protons in the atom must be same.

Therefore, the nucleus can have variation in the number of neutron but not proton for the same carbon sample giving rise to the isotopes of carbon.

Isotopes:

The elements that contains the same atomic number but their mass number is different.