Question #81233

As you know, a neutral atom has equal numbers of protons inside the nucleus and of electrons surrounding the nucleus.

This implies that your element, which has an atomic number equal to #13#, i.e. it has #13# protons inside the nucleus, must have a total of #13# electrons surrounding the nucleus.

Now, each period of the Periodic Table corresponds to an energy shell in which these electrons can reside. The maximum number of electrons that each shell can hold is given by

#color(blue)(ul(color(black)("no. of e"^(-) = 2n^2)))#

Here #n# is the period number, also known as the principal quantum number.

So all you have to do here is to figure out how many full shells are present in your atom. You start with #13# electrons to distribute, so you have

#n = 1 -> "no. of e"^(-) = 2 * 1^2 = 2#

The first energy shell can hold a maximum of #2# electrons, so subtract this from #13# to get #11# electrons left to distribute.

#n = 2 -> "no. of e"^(-) = 2 * 2^2 = 8#

The second energy shell can hold a maximum of #8# electrons, so subtract this from #11# to get #3# electrons left to distribute.

#n = 3 -> "no. of e"^(-) = 2 * 3^2 = 18#

The third energy shell can hold a maximum of #18# 8electrons, but since you only have #3# electrons left to distribute in this energy shell, you can say that these #3# electrons will be the atom's valence electrons*.

You can say that because the valence electrons are located in the outermost energy shell, which in your case is the third energy shell.

You can thus say that your atom has #3# valence electrons located in the third energy shell.