Final answer:
The atomic number refers to the number of protons in an atom's nucleus and is used to define the element's identity. Isotopes have the same atomic number but different mass numbers due to varying numbers of neutrons.
Step-by-step explanation:
The atomic number is the number of protons in the nucleus of an atom, which defines the identity of an element. The correct definition of atomic number for isotopes is The number of protons in an atom; isotopes have the same atomic number but different mass numbers. Therefore, the correct answer to the question provided by the student is option (a). Isotopes are atoms of the same element that have the same number of protons but different numbers of neutrons. This means that while they have the same atomic number, they exhibit different mass numbers. The mass number is the sum of protons and neutrons in the nucleus of an atom. Therefore, isotopes of an element will react chemically in the same way, but they have slightly different physical properties due to the difference in mass.