The possibility of the presence of maximum number of electrons in an atom with the quantum numbers n = 5, ℓ = 2, mℓ = -2, ms = +½. is 8.
Generally, n is called principal quantum number and it indicates the energy levels or energy shells in an atom.
While m represent the magnetic quantum numbers and it shows the total number of electron which share these quantum numbers.
When n = 5 for an electron, then the value of l can be l = {0; 1 ; 2 ; 3; 4} and the values of magnetic quantum numbers lie between -l and + l.
When m1 = 1 then l can be {1 ; 2 ; 3; 4} and similarly, the spin quantum number can have values between m(s) = { +1/2, -1/2}
To put it simply, electrons with opposite spin share only one orbital and thus there will be total 8 electrons.
n = 5, l = 1, m1 = 1 and ms = ± 1/2
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