Option 1: Atoms of different elements may have the same mass numbers. This statement is correct. The mass number of an atom is the total number of protons and neutrons in its nucleus. While atoms of different elements have different numbers of protons, they can have the same number of neutrons, resulting in the same mass number.

Option 2: Atoms of an element may have different mass numbers. This statement is also correct. Isotopes are atoms of the same element that have different numbers of neutrons and therefore different mass numbers. For example, carbon-12 and carbon-14 are both isotopes of carbon, but they have different mass numbers.

Option 3: All the atoms of an element have the same number of protons. This statement is correct. The number of protons in an atom defines its atomic number and determines its elemental identity. Therefore, all atoms of the same element have the same number of protons.

Option 4: All the atoms of an element will always have the same number of neutrons. This statement is not correct. As mentioned earlier, isotopes are atoms of the same element with different numbers of neutrons. Therefore, not all atoms of an element will have the same number of neutrons.