Question

does the atomic number change as an atom gains more neutrons?
yes, since it is gaining mass, its atomic number will change.
no, since the atomic number is based on the number of protons.
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Explanation:

The atomic number of an element is defined by the number of protons in its nucleus. Neutrons do not contribute to the atomic number. Adding neutrons only changes the mass - number (sum of protons and neutrons) and creates isotopes of the element.

Answer:

No, since the atomic number is based on the number of protons.