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

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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

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

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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