If work function of a metal is 2 eV, it means every electron requires only 2 eV to get ejected from the metal surface.
False
Try recalling clearly my friend, we said, the work function is the MINIMUM energy required to pull an electron out. That doesn't imply that every electron needs only that much. Some electrons are more strongly bound, or may lose energy in collisions after they receive energy, and might even not come out.