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

Each electron has its **unique set** that quantum numbers, which means that 2 electrons can share one, two, or even three quantum numbers, but **never all four**.

Now, friend are offered a #color(red)(4)d# **orbital** and asked to find how numerous sets that quantum numbers can define an electron located in together an orbital, or, in other words, how countless *electrons* have the right to 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 actually

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

The **subshell** in i beg your pardon the electron is situated is defined by the *angular magnetic quantum number*, #l#, which for the *fourth energy level* bring away the following 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**, friend will require #l=2#.

The **specific orbital** in i beg your pardon the electron is located is offered by the *magnetic quantum number*, #m_l#. Because that *any* **d-subshell**, the magnetic quantum number deserve to take the values

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

Each that these five values explains one of the 5 **d-orbitals** obtainable in a d-subshell.

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

You are watching: How many d orbitals have n = 4

See more: Third Party Payers Determine The Contents Of A Surgical Package

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

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

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

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

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

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

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

**two electrons**will certainly 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 numbers that deserve to be provided to define an electron situated in among the 5 d-orbitals