The most appropriate statement about the atomic weight of an element is option 2: "Unlike mass number, the atomic weight of an element can be a fraction."

Option 1 states that the atomic weight is the sum total of the number of protons and neutrons present in the atom of the element. This is incorrect. The atomic weight is actually an average value that takes into account the different isotopes of an element, which have varying numbers of neutrons.

Option 3 states that the atomic weight of an element is a whole number. This is incorrect as well, as atomic weights can be decimal numbers.

Option 4 states that the atomic weight of all the atoms in an element is the same. This is incorrect because different isotopes of an element have different atomic weights.

Therefore, option 2 correctly explains that the atomic weight of an element can be a fraction. This is because the atomic weight is calculated as the weighted average of the masses of the different isotopes of an element, taking into account their abundance in nature.