Is it possible for two different atoms of carbon to have different numbers of neutrons in their nuclei? explain.

Yes , it is possible  for two different atoms of carbon to have different numbers of neutrons in their nuclei .

Explanation:

Isotopes -

Atoms of the element with same number of the electrons and protons , but differ in the number of neutrons , are called as the isotopes .

The isotopes of the element have the same number of protons and electrons , hence have the same chemical and physical properties .

Many isotopes occurs naturally .

In case of Carbon ,  

Carbon too have isotopes ,  

i.e.  

Carbon - 13 and Carbon - 14

carbon - 13 , have seven neutrons  

Carbon - 14 , have eight neutrons .

the area between the graph and the t axis