How many electrons in magnesium share the quantum numbers #l=0# and #m_l = 1# ?

1 Answer
Apr 24, 2016

Answer:

Zero.

Explanation:

As you know, four quantum numbers are used to describe the position and spin of an electron in an atom.

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Your goal here is to identify how many electrons located in an atom of magnesium, #"Mg"#, share the quantum numbers

#l = 0" "# and #" " m_l = 1#

Start by writing the complete electron configuration for a neutral atom of magnesium. Magnesium is located in period 3, group 2 of the periodic table and has an atomic number equal to #12#.

This means that a neutral magnesium atom will have a total of #12# electrons surrounding its nucleus. Its electron configuration would look like this

#"Mg: " 1s^2 2s^2 2p^6 3s^2#

Now, the angular momentum quantum number, #l#, tells you the subshell in which the electron resides. The possible values of #l#, which depend on the value of #n#, the principal quantum number, correspond to

  • # l = 0 -># the s-subshell
  • #l = 1 -># the p-subshell
  • #l=2 -># the d-subshell
  • #l =3 -># the f-subshell
    #vdots#

In your case, the value #l=0# corresponds to the s-subshell.

Now, the magnetic quantum number, #m_l#, tells you the exact orbital in which the electron resides. As you can see, #m_l# depends on the value of #l#

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

The only possible value for #m_l# that would correspond to an electron located in an s-subshell, regardless of energy level, is

#m_l = 0 -># corresponds to the s-orbital

You can thus say that no electrons share the quantum numbers #l=0# and #m_l = 1#, in a magnesium atom, or in any atom for that matter.

You will never find an atom in which an electron has the quantum number #l=0# and #m_l = 1# because the only possible value for #m_l# when #l=0# is #m_l = 0#.

#color(white)(a)#
ALTERNATIVE INTERPRETATION

Just in case you had to determine how many electrons share the quantum number #l=0# and how many share the quantum number #m_l = 1#, I'll write out a quick explanation here.

If you're looking for electrons that have #l=0#, you're essentially looking for electrons located in the s-subshell. As you can see by looking at magnesium's electron configuration, the atom has three s-subshells filled with electrons

  • #1s^2 -># two electrons located in the s-subshell of the first energy level
  • #2s^2 -># two electrons located in the s-subshell of the second energy level
  • #3s^2 -># two electrons located in the s-subshell of the third energy level

Therefore, a total of six electrons have #l=0# in a neutral magnesium atom.

Now, in a magnesium atom, #m_l = 1# corresponds exclusively to electrons located in one of the three orbitals located in the p-subshell.

More specifically, you have

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

A magnesium atom has the p-subshell of the second energy level completely filled with electrons, which means that the #p_z# orbital holds two electrons.

Therefore, a total of two electrons have #m_l = 1# in a neutral magnesium atom.