# Which set(s) of of quantum numbers describe a 4d orbital?

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A total of

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As you know, we use **four quantum numbers** to describe the position and spin of an electron in an atom.

Each electron has its **unique set** of quantum numbers, which means that two electrons can share one, two, or even three quantum numbers, but **never all four**.

Now, you are given a **orbital** and asked to find how many sets of quantum numbers can describe an electron located in such an orbital, or, in other words, how many *electrons* can occupy a **orbital**.

So, the *principal quantum number*, **energy level** on which the electron is located. In this case, you have

#n = color(red)(4) -># the electron is located on thefourth energy level

The **subshell** in which the electron is located is described by the *angular magnetic quantum number*, *fourth energy level* takes the following values

#l=0 -># thes-subshell#l=1 -># thep-subshell#l=2 -># thed-subshell#l=3 -># thef-subshell

Since you're looking for the **d-subshell**, you will need

The **specific orbital** in which the electron is located is given by the *magnetic quantum number*, *any* **d-subshell**, the magnetic quantum number can take the values

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

Each of these five values describes one of the five **d-orbitals** available in a d-subshell.

Finally ,the *spin quantum number*, *spin-down* and *spin-up*.

Now, since each orbital can hold a maximum of **two electrons**, one with spin-up and one with spin-down, it follows that the **d-obitals** can hold a total of

#"2 e"^(-)"/ orbital" xx "5 orbitals" = "10 e"^(-)#

Each of these ten electrons will have its **unique set** of four quantum numbers.

all the ten electronswill share the principal and angular momentum quantum numbers

#n= color(red)(4)" "# and#" "l=2#

five electronswill share the spin quantum number

#m_s = -1/2" "# or#" "m_s = +1/2#

two electronswill share the magnetic quantum number

#m_l = -2" "# or#" "m_l = -1" "# or#" "m_l = color(white)(-)0" "# or#" "m_l = +1" "# or#" "m_l = +2#

You will thus have **sets** of quantum numbers that can be used to describe an electron located in one of the five d-orbitals

#n=color(red)(4), l=2, m_l = -2, m_s = +1/2#

#n=color(red)(4), l=2, m_l = -2, m_s = -1/2#

#n=color(red)(4), l=2, m_l = -1, m_s = +1/2#

#n=color(red)(4), l=2, m_l = -1, m_s = -1/2#

#n=color(red)(4), l=2, m_l = color(white)(-)0, m_s = +1/2#

#n=color(red)(4), l=2, m_l = color(white)(-)0, m_s = -1/2#

#n=color(red)(4), l=2, m_l = +1, m_s = +1/2#

#n=color(red)(4), l=2, m_l = +1, m_s = -1/2#

#n=color(red)(4), l=2, m_l = +2, m_s = +1/2#

#n=color(red)(4), l=2, m_l = +2, m_s = -1/2#

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