# Question #10924

##### 1 Answer

Here's what I got.

#### Explanation:

I'm guessing that you want to figure out a possible set of quantum numbers that can describe an electron located in the **subshell**.

For starters, you should know that we can use a total of **quantum numbers** to describe the *location* and *spin* of an electron inside an atom.

Now, the **subshell** in which an electron resides is given by the *angular momentum quantum number*,

#l = 0 -># designates thes subshell#l=1 -># designates thep subshell#l = 2 -># designates thed subshell#l = 3 -># designates thef subshell

#vdots#

and so on. So in your case, **all the electrons** that can reside in the **subshell** will have

#l = 3#

Notice that the value of the angular momentum quantum number depends on the value of the *principal quantum number*,

This means that in order for your electrons to have access to the **fifth energy level**, so

#n = color(red)(5)#

The **subshell** contains a total of **orbitals**, all described by a distinct value of the *magnetic quantum number*,

#m_l = {-3, - 2, -1, 0, 1, 2, 3}#

The *spin quantum number*,

#m_s = { -1/2, + 1/2}#

Since each *orbital* can hold a maximum of **electrons** of opposite spins, i.e. of opposite **Pauli's Exclusion Principle** here--you can say that the **subshell** can hold a maximum of

#7 color(red)(cancel(color(black)("orbitals"))) * "2 e"^(-)/(1color(red)(cancel(color(black)("orbital")))) = "14 e"^(-)#

This implies that you can write a total of **distinct** quantum number sets to describe one of the

For example, you can have

#n =5 , l= 3 , m_l = -3, m_s = +1/2# #n = 5, l = 3, m_l = 0, m_s = -1/2# #n = 5, l = 3, m_l = 2, m_s = +1/2# #n = 5, l = 3, m_l = -1, m_s = -1/2#

and so on. Notice that **all the**