No, carbon-14 and nitrogen-14 are not the same element, despite having the same mass number. The identity of an element is determined by its atomic number, which corresponds to the number of protons in the nucleus.
Carbon-14 (C-14) has an atomic number of 6, indicating that it has 6 protons in its nucleus. On the other hand, nitrogen-14 (N-14) has an atomic number of 7, indicating that it has 7 protons.
While both carbon-14 and nitrogen-14 have a mass number of 14 (which is the sum of protons and neutrons), they have different atomic numbers, meaning they have different numbers of protons and therefore belong to different elements. The atomic number is the fundamental property that distinguishes one element from another, regardless of the mass number.