# How many electrons in an atom can have #n=7# and #m_l = +3# ?

##### 1 Answer

#### Explanation:

The trick here is to focus on the value of the *magnetic quantum number*, **orbital** in which an electron resides inside an atom.

You know that **every value** the magnetic quantum number takes represents an **orbital**. You also know that every orbital can hold a maximum of **electrons**.

You can thus say that

#m_l = +3#

can be shared by a maximum of **electrons per subshell**.

Now, we use a total of four quantum numbers to describe the position and spin of an electron inside an atom.

As you can see, the value of the magnetic quantum number depends on the value of the *angular momentum quantum number*, *principal quantum number*,

More specifically, you know that

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

and that

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

For

#l = {0, 1, 2, 3, 4, 5, 6}#

Notice that you can only have **subshells** can hold orbitals that have

#l = {color(red)(cancel(color(black)(0, 1, 2))), 3, 4, 5, 6}#

You can thus say that you have

#l = 3#

#m_l = {-3,-2,-1,0,+1,+2,color(red)(+3)}#

#l = 4#

#m_l = {-4, -3,-2,-1,0,+1,+2,color(red)(+3), +4}#

#l = 5#

#m_l = {-5, -4, -3,-2,-1,0,+1,+2,color(red)(+3), +4, +5}#

#l = 6#

#m_l = {-6, -5, -4, -3,-2,-1,0,+1,+2,color(red)(+3), +4, +5, +6}#

So, you know that for **orbitals** described by **electrons**, you will have

#4 color(red)(cancel(color(black)("orbitals"))) * "2 e"^(-)/(1color(red)(cancel(color(black)("orbital")))) = "8 e"^(-)#

Therefore, you know that a maximum of **electrons** can share these two quantum numbers

#n=7, m_l = +3#