Question

Which of the following is a possible set of quantum numbers for an electron n, l, m subscript l, m subscript s?

(1, 1, 0, +½)
(2, 1, 2, +½)
(3, 2, 0, -½)
(3, -2, 1, -½)

Answer 1

@Abhisar

Answer 2

@FriedRice

Answer 3

For the set of quantum numbers (n, l, m, s), the following rules apply:

- The principal quantum number, n, can take on any whole number value from 1 (the lowest available energy level up until infinity. It defines the energy level the orbital which contains the electron is at.
- The orbital angular momentum quantum number, l, defines the shape of this orbital. The list of acceptable l values goes from 0,1,2....n-1, where n is the value we used in the last stage (0 = s orbital, 1 = p, 2 = d, 3 = f, 4 = g, 5 =h,....).
-The magnetic quantum number, m subscript l, defines the orientation/position of this orbital. Given l values we have, for each one the list of possible orientations are represented by values from -l,....,-1,0,1,....l.
-The spin quantum number, s, defines the spin the electron has in its given orbital. The Pauli Exclusion Principle states that there can only ever be a maximum of 2 electrons in a given orbital, and that they must have opposite spins. We use the values +1/2 and -1/2 to represent these opposite spins, so an electron could have either one or the other. It is not dependent on either n, l, or m subscript l.

I'll do out the first one as an example, (1,1,0, +1/2). We see that the first quantum number, n, is 1, which is OK from the rules above. The second quantum, number, the orbital angular momentum, l, is also 1. But, our rules say that this can only be a whole number between 0 and n-1 (i.e. it must be zero, in this case). So, the first set is not possible for an electron.

Work your way through them using the rules and different steps until you meet a correct set. It can be quite confusing at first, but if you take your time it should be OK. Hope that helps! :)

Answer 4

Thank you soooo much!

Answer 5

No problem. Best of luck with it! :)

Answer 6

:-)