What is the correct set of quantum numbers (n, l, ml, ms) for the highest energy electron in the ground state of tin, Sn?
1 Answer
Here's what I got.
Explanation:
Your starting point here will be tin's electron configuration.
Tin,
So, the electron configuration for tin looks like this - I'll use the noble gas shorthand notation
#"Sn: " ["Kr"] 4d^10 color(red)(5)s^2 color(red)(5)p^2#
Now, you're looking for the electron that's highest in energy. Notice that you have two electrons that match this profile, both located in the 5p-subshell.
As you know, four quantum numbers are used to describe the location and spin of an electron in an atom.
So, let's start with the first one, the principal quantum number,
In your case, the highest energy level is equal to
#n = color(red)(5)#
Next, the angular momentum quantum number,
#l=0 -># the s-subshell#l=1 -># the p-subshell#l=2 -># the d-subshell#l=3 -># the f-subshell
and so on. In your case, you're looking for the value of
# l = 1#
Next, the magnetic quantum number,
More specifically, you need to know that all degenerate orbitals must be half-filled before any of them can take in a second electron. Furthermore, all half-filled degenerate orbitals contain electrons of the same spin.
The p-subshell contains a total of three orbitals, given by the values of
#m_l = -1 -># the#5p_x# orbital#m_l = color(white)(-)0 -># the#5p_y# orbital#m_l = color(white)(-)1 -># the#5p_z# orbital
Since tin's 5p-subshell contains two electrons, it follows that these electrons will occupy distinct 5p-orbitals. More specifically, you will have
#m_l = -1 -># one electron in the#5p_x# orbital
#m_l = color(white)(-)0 -># one electron in the#5p_y# orbital
Finally, the spin quantum number,
Therefore, the quantum number sets for the two highest-energy electrons found in a tin atom are
#n=5, l =1, m_l = -1, m_s = +1/2#
This electron is located on the fifth energy level, in the p-subshell, in the
#n=5, l=1, m_l = 0, m_s = +1/2#
This electron is located on the fifth energy level, in the p-subshell, in the