What is a set of four quantum numbers that could represent the last electron added (using the Aufbau principle) to the Cl atom?

1 Answer
Jul 3, 2016

Answer:

Here's what I got.

Explanation:

Your starting point here will be the electron configuration of a neutral chlorine atom.

Chlorine is located in period 3, group 17 of the periodic table and has an atomic number equal to #17#. This tells you that the electron configuration of a chlorine atom must account for a total of #17# electrons that surround the nucleus of the atom.

The electron configuration of a chlorine atom looks like this

#"Cl: " 1s^2 2s^2 2p^6 3s^2 3p^5#

Now, the last subshell to be filled with electrons, which is also the highest in energy, is the #3p# subshell.

As you can see from the electron configuration, this subshell contains a total of #5# electrons. These electrons are distributed in #3# orbitals labelled #3p_x#, #3p_y#, and #3p_z#.

As you know, we can use a set of four quantum numbers to describe the location and spin of an electron in an atom

figures.boundless.com

Let's start with the principal quantum number, #n#. Since this last electron is added to the third energy level, you will have

#n=3 -># the third energy level

The angular momentum quantum number, #l#, describes the subshell in which the electron is located. In this case, the last electron is added to the #3p# subshell, so you will have

#l=1 -> # the p-subshell

Now, this is where things can get a little tricky. According to Hund's Rule, every orbital in a given subshell must be occupied with #1# electron before a second electron is added to any of these orbitals.

You know that the #3p# subshell contains a total fo #5# electrons. In this case, each of the three #3p# orbitals will first be occupied with a spin-up electron. This will account for #3# of the #5# electrons.

After this happens, the second-to-last electron will occupy the #3p_x# orbital, this time having spin-down.

Finally, the last electron to be added will be placed in the #3p_z# orbital, once again having spin-down. Here's a diagram showing the electron configuration of chlorine, with the last electron added highlighted

enter image source here

So, the magnetic quantum number, #m_l#, tells you the specific orbital in which the electron is located. By convention, you have

  • #m_l = -1 -># the #3p_x# orbital
  • #m_l = color(white)(-)0 -># the #3p_z# orbital
  • #m_l = +1 -># the #3p_y# orbital

In this case, you would have

#m_l = 0 -># the #3p_z# orbital

Finally, the spin quantum number, #m_s#, tells you the spin of the electron. In this case, you have

#m_s = -1/2 -># a spin-down electron

Therefore, a possible quantum number set for the last electron added to a chlorine atom is

#color(green)(|bar(ul(color(white)(a/a)color(black)(n=3, l=1, m_l = 0, m_s = -1/2)color(white)(a/a)|)))#