# Question #a47b4

##### 1 Answer

Two electrons.

#### Explanation:

As you know, the *principal quantum number*, *angular momentum quantum number*, **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*,

#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# cannotbe equal to#n# .

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

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

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

Not possible because#l# .cannothave a negative value

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

Not possible because#l# .cannothave a negative value

Now, the number of values that the *magnetic quantum number*, **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#

Asingle orbitalis located in the#s# .subshell

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

This implies that the total number of electrons that can have

#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 **subshell**, in the **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#