Question #51981

1 Answer
Sep 15, 2017

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