An element's atomic number is 74. How many protons would an atom of this element have?

Atomic number of an atom equals to the number of nucleus in the nucleus of the atom. Therefore, the answer is 74.

The proton of an element is never changed. No matter if it's an atom or ion. It's like an ID number for an element. It defines the type of element. Don't mix up atomic number with mass number though, mass number is the total sum of of the number of protons and neutrons in an atom.

Theres one more subatomic particle in an atom, that is electrons. But since they're too light, they won't be counted in mass. Also, the number of electrons in an atom equals to the number of proton, also the atomic number. If the number of electrons is different, it's no longer an atom, but an ion.