A an excellent place to start once trying to number out the electron configuration of one ion is the electron construction of the neutral parent atom.

In this case, titanium, #"Ti"#, is located in duration 4, group 4 of the regular table and has an atomic variety of #22#.

This means that a neutral titanium atom will contain #22# proton in that nucleus and #22# electrons surrounding its nucleus.

Therefore, the electron construction of a neutral titanium atom need to account because that #22# electrons. Consequently, the electron configuration of the titanium(II) cation, #"Ti"^(2+)#, have to account for #20# electrons, because this cation is developed when a neutral titanium atom loses #2# electrons.

The electron construction of a neutral titanium atom looks favor this

#"Ti: " 1s^2 2s^2 2p^6 3s^2 3p^6 4s^2 3d^2#

Now, it"s essential to save in mind that this notation because that the electron construction is valuable when adding electrons to build an atom "from scratch" because in the case, the #4s# orbital is fill before the #3d# orbitals.

That happens since the empty #3d# orbitals room actually higher in energy than the empty #4s# orbital, as viewed here

However, as soon as the #4s# orbit is filled, it becomes higher in power than the #3d# orbitals.

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This way that when titanium loses electrons, that does so from the #4s# orbital first.

#"Ti: " 1s^2 2s^2 2p^6 3s^2 3p^6 3d^2 4s^2#

Therefore, the 2 electrons that are lost when the #"Ti"^(2+)# is formed will come indigenous the #4s# orbital, which means that the electron configuration of the cation is

#color(green)(|bar(ul(color(white)(a/a)color(black)("Ti"^(2+): 1s^2 2s^2 2p^6 3s^2 3p^6 3d^2)color(white)(a/a)|)))#

If you want, you have the right to use the noble gas shorthand notation to write

#color(green)(|bar(ul(color(white)(a/a)color(black)("Ti"^(2+): <"Ar"> 3d^2)color(white)(a/a)|)))#

Here #<"Ar"># to represent the electron configuration of argon, the noble gas the comes instantly before titanium in the regular table.