# Question #86f7b

##### 1 Answer

#### Explanation:

The question essentially wants you to find **half** of the **maximum number of electrons** that can reside on the third energy level, i.e. the *number of orbitals* present on this energy level.

As you know, the *spin quantum number*, **spin** of the electron, can take two possible values

#m_s = +1/2 -># the electron hasspin-up#m_2 = -1/2 -># the electron ahsspin-down

According to *Pauli's Exclusion Principle*, each **individual orbital** can hold a maximum of two electrons, one having spin-up and the other spin-down.

This implies that in order to find the total number of electrons that can have **total number of electrons** that reside on the third energy level and divide it by

Now, the **total number of electrons** that can reside in a given energy level is equal to

#"total no. of electrons" = 2n^2#

Here *principal quantum number*, represents the **energy level** on which the electron resides.

In your case, you have

#"total no. of electrons" = 2 * 3^2 = 18#

This means that the number of electrons that can have

#"18 e"^(-)/2 = "9 e"^(-)#

In other words, the third energy level can hold **orbitals**.