Question

List a possible set of four quantum numbers (n, ℓ, mℓ, ms) in order, for the highest energy electron in gallium, Ga.

Answer 1

You have to look in your periodic table where the Ga is located and find out many electrons it has. Gallium is the element number 31.
You can write the electron configuration
1s2 2s2 2p6 3s2 3p6 4s2 3d10 4p1
or
[Ar] 4s2 3d10 4p1
then the electron with the highest energy will be the one in the 4p1, or the last in the electronic configuration.
the "n" quantum number is indicated by the number 4
the "ℓ" quantum number can have values from 0 to n-1, in this case is "p" that is equivalent to "1"
s= 0
p= 1
d= 2
f= 3
the "mℓ" number can have values from -ℓ to +ℓ
in the case of the Ga, ℓ=1 then mℓ can adopt the values of -1,0,+1
Finally the "ms" number can have only two different values +1/2, and -1/2. When filling the electrons in the orbitals first will fill one + 1/2 in each orbital of the ℓ and then pair them with the second electron with the -1/2 magnetic spin

Answer 2

thank you for your help