The atomic number of an element is defined by the number of protons in its nucleus. Since the element in question has 8 protons, its atomic number is 8.
The atomic mass is approximately equal to the total number of protons and neutrons in the nucleus. This element has 8 protons and 8 neutrons, so its atomic mass is 8 protons + 8 neutrons = 16.
Therefore, the correct answer is: C. The atomic number is 8 and the atomic mass is 16.