# What could the fourth quantum number of a #2s^2# electron be?

##### 1 Answer

#### Explanation:

As you know, a total of **four quantum numbers** are used to describe the positions and the spin of an electron in an atom.

In your case, you must decide which possible values can be assigned to the **fourth quantum number** of an electron that resides in a

The *principal quantum number* describes the **energy level**, or **shell**, on which the electron resides. In this case, the electron is located on the *second energy level*, so

The *angular momentum quantum number*, **subshell** in which the electron is located. For an **s-orbital**, the angular momentum quantum number is equal to

The *magnetic quantum number*, **specific orbital** in which you can find the electron. For an **s-orbital**, the magnetic quantum number can only take the value

#m_l = -l, -(l-1), ..., -1, 0, 1, ..., (l-1), l#

Finally, the *spin quantum number*,

Now, the **s-orbital** can hold a maximum of **two electrons**. The first electron will have

The **first electron** to occupy the 2s-orbital would be represented using the notation **second electron** would be represented using the notation

This means that the fourth quantum number for a

#m_s = -1/2 -># spin-down

This implies that the 2s-orbital already contains an electron that has

#m_s = +1/2 -># spin-up

You can put all this together to find the *quantum number set* that describes the

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