# What is a possible set of four quantum numbers (n,l ,ml ,ms ) for the highest-energy electron in Ga?

##### 1 Answer

#### Answer:

Here's what I got.

#### Explanation:

Your starting point here will be gallium's electron configuration.

Gallium, *neutral* gallium atom will have a total of

The electron configuration of gallium looks like this - I'll use the noble gas shorthand notation

#"Ga: " ["Ar"]3d^10 4s^2 4p^1#

Now, you're interested in finding the possible sets of quantum numbers that describe the **highest-energy** electron that belongs to a gallium atom.

As you know, the quantum numbers are defined

So, the highest-energy electron found in gallium is located in a **4p-orbital**, which means that right from the start you know that the value of its *principal quantum number*,

Now for the *angular momentum quantum number*, **subshell** in which the electron resides.

Notice that the fourth energy level has total of **subshells**, each corresponding to a different value of

#l =0 -># the s-subhell#l = 1 -># the p-subshell#l=2 -># the d-subshell#l=3 -># the f-subshell

SInce your electron is located in the **p-subshell**, it follows that its

The *magnetic quantum number*, **in which orbital** you can expect to find the electron.

For the p-subshell,

#m_l = -1 -># the#p_x# orbital#m_l = color(white)(-)0 -># the#p_y# orbital#m_l = color(white)(-)1 -># the#p_z# orbital

Since the p-subshell only contains one electron, you can place it in the first available p-orbital, which is

Finally, the *spin quantum number*, **two possible values**

#m_s = -1/2 -># a spin-down electron#m_s = +1/2 -># a spin-up electron

Since the orbital only contains **one electron**, it follows that it could be either spin-up or spin-down, so you get two possible sets of quantum numbers

#n=4 -> l=1 -> m_; = -1 -> m_2 = -1/2#

A *spin-down* electron located in the

#n=4 -> l=1 -> m_; = -1 -> m_2 = +1/2#

A *spin-up* electron located in the