Question

Question #a47b4

Answer 1

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}`

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`