# How many electrons have...?

##
#a)# #n = 4# , #l = 2#

#b)# #n = 4# , #l = 2# , #m_l = +2#

#c)# #n = 4# , #l = 2# , #m_l = +2# , #m_s = +1/2#

##### 1 Answer

The answers would be **a) 10 electrons**, **b) 2 electrons**, and **c) 1 electron**.

I assume you're familiar with quantum numbers, so I won't go into too much detail about them.

So, here are the four quantum numbers you have to work with

Let's start with point **a)**. Since you already know that **n = 4** and **l = 2**, you only have to decide the possible values for the magentic quantum number,

Since the magnetic quantum number can only go from

#m_l = -2, -1, 0, +1, +2#

SInce each of these orbitals can hold a maximum of two electrons, one having spin-up and one having spin-down, a total of **10 electrons** can share the quantum numbers **n = 4** and **l = 2**

#m_l = -2 => m_s = +- 1/2#

#m_l = -1 => m_s = +- 1/2#

#m_l = 0 => m_s = +- 1/2#

#m_l = +1 => m_s = +- 1/2#

#m_l = +2 => m_s = +- 1/2#

On to point **b)**. Now you know that **n = 4**, **l = 2**, and **2**, which means that only **2 electrons**, one having spin-up and one having spin-down, can share these three quantum number values.

#m_s = +- 1/2#

FInally, point **c)**. Because every electron has a *specific set of quantum numbers* that describes its position around the nucleus, the values given to you for all the four quantum numbers can only describe **1 electron**.