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

Each electron has its **unique set** that quantum numbers, which means that two electrons deserve to share one, two, or also three quantum numbers, yet **never every four**.

Now, you are provided a #color(red)(4)d# **orbital** and also asked to discover how numerous sets of quantum numbers can explain an electron situated in together an orbital, or, in other words, how plenty of *electrons* can occupy a #color(red)(4)d# **orbital**.

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

#n = color(red)(4) -># *the electron is located on the fourth power level*

The **subshell** in i beg your pardon the electron is located is defined by the *angular magnetic quantum number*, #l#, which for the *fourth power level* take away the adhering to values

*the*#l=1 ->#

**s-subshell***the*#l=2 ->#

**p-subshell***the*#l=3 ->#

**d-subshell***the*

**f-subshell**Since you"re in search of the **d-subshell**, girlfriend will require #l=2#.

The **specific orbital** in i m sorry the electron is situated is given by the *magnetic quantum number*, #m_l#. For *any* **d-subshell**, the magnetic quantum number can take the values

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

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

Finally ,the *spin quantum number*, #m_s#, have the right to only take 2 values, #-1/2# for an electron that has *spin-down* and also #+1/2# for an electron that has actually *spin-up*.

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Now, because each orbital can hold a preferably of **two electrons**, one with spin-up and one through spin-down, it follows that the **d-obitals** have the right to hold a complete of

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

Each of this ten electron will have actually its **unique set** of four quantum numbers.

**all the ten electrons**will certainly share the principal and angular inert quantum numbers

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

**five electrons**will share the rotate quantum number

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

**two electrons**will 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 #10# **sets** that quantum number that have the right to be offered to explain an electron located in one of the 5 d-orbitals