No, not all carbon atoms have the same atomic mass. Carbon is an element with multiple isotopes, which means that different atoms of carbon can have different numbers of neutrons in their nuclei while retaining the same number of protons.
The most abundant and stable isotope of carbon is carbon-12, which has 6 protons and 6 neutrons, giving it an atomic mass of approximately 12 atomic mass units (u). However, there are also two other naturally occurring isotopes of carbon: carbon-13 and carbon-14.
Carbon-13 has 6 protons and 7 neutrons, resulting in an atomic mass of approximately 13.003 u. Carbon-14, on the other hand, has 6 protons and 8 neutrons, giving it an atomic mass of approximately 14.003 u.
Since the isotopes of carbon occur in different proportions in nature, the atomic mass of carbon, as listed on the periodic table, is the weighted average of the masses of all the naturally occurring isotopes. This average atomic mass is approximately 12.01 u.