Which of the following is not a valid set of four quantum numbers? How can you determine this?

a. 2,0,0, + 1/2
b. 2,1,0, -1/2
c. 3,1, -1, -1/2
d. 1,0,0, +1/2
e. 1,1,0, +1/2?

1 Answer
Jul 1, 2016

Answer:

The answer is #(e)#.

Explanation:

Start by making sure that you're familiar with the valid values each quantum number can take.

figures.boundless.com

As you can see, the principal quantum number, #n#, determines the possible values of the angular momentum quantum number, #l#, which in turn determines the possible values of the magnetic quantum number, #m_l#.

The spin quantum number is independent of the of the values taken by the other three quantum numbers and can only have two possible values, #+1/2# and #-1/2#.

Now, take a look at the relationship between the value of #n# and the value of #l# for each of those five sets of quantum numbers.

#(a)" "n=2, l=0, m_l = 0, m_s = +1/2" "color(green)(sqrt())#

This set is valid because #l# can take the value #0# when #n=2#. The same can be said about #m_l#, which can take the value #0# when #l=0#.

This quantum number set represents an electron located on the second energy level, in the s-subshell, in the #2s# orbital, that has spin-up.

#(b)" " n=2, l=1, m_l = 0, m_s = -1/2" "color(green)(sqrt())#

This set is valid because #l=1# is still within the accepted value of

#l = 0, 1, ..., (n-1)#

when #n=2#. This time, the set represents an electron that is located on the second energy level, in the p-subshell, in the #2p_z# orbital, that has spin-down.

#(c)" "n=3, l=1, m_l=-1, m_s = -1/2" "color(green)(sqrt())#

Once again, you're dealing with a valid set. All the quantum numbers are well within their accepted values. Notice that when #l=1#, you can have

#m_l = {-1, color(white)(-)0, +1}#

This set represents an electron located on the third energy level, in the p-subshell, in the #3p_x# orbital, that has spin-down.

#(d)" "n=1, l=0, m_l = 0, m_s = +1/2" "color(green)(sqrt())#

This set is valid and it represents an electron located on the first energy level, in the s-subshell, in the #1s# orbital, that has spin-up.

#(e)" "n=1, l=1, m_l = 0, m_s = +1/2 " "color(red)(xx)#

This is not a valid set of quantum numbers. Notice that #l# cannot take the value of #n#, but here

#n=1" "# and #" "l=1#

This means that the set cannot describe an electron located in an atom, i.e. it's not a valid set.