Question #a47b4

1 Answer
Oct 5, 2017

Answer:

Two electrons.

Explanation:

As you know, the principal quantum number, #n#, and the angular momentum quantum number, #l#, can only take positive values, so you only have a handful of possibilities for

#n + l = 2#

The angular momentum quantum number depends on the principal quantum number as follows

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

You know that zinc, #"Zn"#, is located in the fourth period of the Periodic Table. This implies that the electrons located in an atom of zinc will have

#n = {1, 2, 3, 4}#

http://www.knowledgedoor.com/2/elements_handbook/zinc.html

This means that you can have

  • #n + l = 2 " "-> " "color(red)(cancel(color(black)(n = 1 implies l= 1)))#

Not possible because #l# cannot be equal to #n#.

  • #n +l = 2" " -> " " n = 2 implies l = 0" " " "color(green)(sqrt())#

These electrons will be located on the second energy level, in the #s# subshell.

  • #n + l = 2 " "-> " "color(red)(cancel(color(black)(n = 3 implies l= -1)))#

Not possible because #l# cannot have a negative value.

  • #n + l = 2 " "-> " "color(red)(cancel(color(black)(n = 4 implies l= -2)))#

Not possible because #l# cannot have a negative value.

Now, the number of values that the magnetic quantum number, #m_l#, can take will give you the number of orbitals located in each subshell.

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

You will have

#l = 0 implies m_l = 0#

A single orbital is located in the #s# subshell.

As you know, each orbital can hold a maximum of #2# electrons of opposite spins.

This implies that the total number of electrons that can have #n + l = 2# in a zinc atom is

#1 color(red)(cancel(color(black)("orbital"))) * "2 e"^(-)/(1color(red)(cancel(color(black)("orbital")))) = color(darkgreen)(ul(color(black)("2 e"^(-))))#

Both electrons will be located in the #2s# subshell, in the #2s# orbital, and have opposite spins. The complete sets of quantum numbers for these electrons will be

#n = 2, l= 0, m_l = 0, m_s = +1/2#

#n = 2, l = 0, m_l = 0, m_s = -1/2#