Final answer:
The claim is false as atoms of the same element can have varying numbers of neutrons, leading to different isotopes with the same number of protons but different mass numbers.
Step-by-step explanation:
The statement that all atoms of the same element have the same number of neutrons is false. Atoms of the same element are characterized by having the same number of protons in their nuclei; this is what defines them as the same element. However, these atoms can have varying numbers of neutrons, which leads to different isotopes of that element. Isotopes have the same atomic number due to having the same number of protons, but they have different mass numbers because of the difference in their neutron count. An example would be carbon, which has isotopes with six, seven, or eight neutrons while always having six protons.