As friend know, we use four quantum numbers to explain the position and also spin of an electron in an atom.

Each electron has its unique set the quantum numbers, which method that 2 electrons deserve to share one, two, or even three quantum numbers, but never every four.

Now, friend are offered a #color(red)(4)d# orbital and asked to discover how many sets the quantum number can define an electron situated in such an orbital, or, in various other words, how numerous electrons deserve to occupy a #color(red)(4)d# orbital.

So, the principal quantum number, #n#, defines the energy level on i m sorry the electron is located. In this case, you have actually

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

The subshell in i beg your pardon the electron is situated is defined by the angular magnetic quantum number, #l#, which because that the fourth energy level bring away the complying with values

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

Since you"re trying to find the d-subshell, girlfriend will need #l=2#.

The specific orbital in which the electron is situated is given by the magnetic quantum number, #m_l#. For any d-subshell, the magnetic quantum number deserve to take the values

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

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

Finally ,the spin quantum number, #m_s#, can only take two values, #-1/2# because that an electron that has spin-down and also #+1/2# for an electron that has spin-up.

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Now, since each orbital can hold a preferably of two electrons, one with spin-up and one through spin-down, it adheres to that the d-obitals can hold a complete of

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

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

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

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

five electrons will certainly share the rotate 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 certainly thus have #10# sets that quantum numbers that have the right to be supplied to explain an electron situated in one of the 5 d-orbitals