What element is represented by ##[Ar]4s^2 3d^10 4p^1##?

The element is gallium (Ga), which has the 31.

##["Ar"]"4s"^2"3d"^10"4p"^1"##

If you look up the element argon, Ar, on , you will see that its atomic number is 18, which means that it has 18 protons in its atomic nuclei. In a neutral atom, the numbers of protons and electrons are equal. So a neutral Ar atom has 18 electrons. Therefore, the symbol ##["Ar"]## in the given represents 18 electrons. Add the additional electrons represented by the superscripts in the rest of the electron configuration, and you get 31 electrons ##(18+13=31)##.