Question #51981

1 Answer
Sep 15, 2017

Answer:

#n=3, l=1, m_l = -1, m_s = +1/2#

Explanation:

For starters, grab a Periodic Table and look for silicon, #"Si"#. You should find it in period 3, group 14.

http://www.learnabout-electronics.org/Semiconductors/semiconductors_01.php

Now, notice that silicon has an atomic number equal to #14#. This means that a neutral silicon atom has #14# protons inside its nucleus and #14# electrons surrounding its nucleus.

In your case, you need to find the set of quantum numbers that describe the #"13th"# electron in a neutral silicon atom.

To do that, use the fact that the Periodic Table can be organized in blocks.

https://chem.libretexts.org/Textbook_Maps/Introductory_Chemistry_Textbook_Maps

In your case, the last #2# electrons added to a neutral silicon atom are located in the #p# block.

This means that these electrons will have the angular momentum quantum number, #l#, equal to #1#.

#l = 1 -># describes an electron located in the #p# block

The period in which silicon is located will give you the value of the principal quantum number, #n#. In your case, silicon is located in period #3#, so the principal quantum number will be equal to #3#.

#n = 3 -># describes an electron located on the third energy level

Now, in order to find the magnetic quantum number, #m_l#, which gives you the orientation of the orbital in which the electron is located, you need to use the fact that the #p# subshell can hold a total of three #p# orbitals.

#l = 1 implies m_l = { (-1 -> "the p"_xcolor(white)(.)"orbital"), (color(white)(+)0 -> "the p"_zcolor(white)(.)"orbital"), (+1 -> "the p"_ycolor(white)(.)"orbital") :}#

In your case, the #"13th"# electron will be added to the first empty #3p# orbital, which, by convention, will have #m_l = -1#.

#m_l = -1 -># describes and electron located in a #p_x# orbital

Finally, the spin quantum number, #m_s#, which tells you the spin of the electron, is equal to

#m_s = {( +1/2 -> "the electron is added to an empty orbital"), ( -1/2 -> "the electron is added to a half-filled orbital") :}#

Since the #"13th"# is added to the first empty #3p_x# orbital, you can say that you have

#m_s = +1/2 -># describes and electron that has spin-up

Therefore, you can say that the quantum number set that describes the #"13th"# electron in a neutral silicon atom is

#n = 3, l= 1, m_l = -1, m_s = +1/2#

This electron is located on the third energy level, in the #3p# subshell, in the #3p_x# orbital, and has spin-up