DETERMINE IF THE GIVEN QUANTUM NUMBERS ARE VALID

Question

Determine whether the following sets of quantum numbers are valid or not. If valid, identify the atomic orbital being described and explain it briefly. Any explanations would help me a lot because I'm still confused about this topic. Thank you!

1. {2,2,0,-1/2}
2. {5,3,-1,+1/2}
3. {2,1,-1,+1/2}

Answer 1

The first number is the energy level.m (n). Next is l and this tells you the shape of the orbital, ie tells you if it’s a p, d, etc. It can have values of 0,1,2,3…

s = 0

p = 1

d = 2

f = 3

etc

Next is m and this has values of-l to + l and tells you where the electron is in the orbital. Finally you have spin (s) and it can be +1/2 or -1/2

1. {2,2,0,-1/2} - invalid because n=2 and l=2 meaning it’s a d orbital which can’t be when n=2.
2. {5,3,-1,+1/2} - valid - the orbital is an f orbital since l=3 and it’s in the 5th energy level. The electron being described is the first one since ml=-1.
3. {2,1,-1,+1/2} - valid - the orbital is a p orbital since l=1 and it’s in the 2nd energy level (n=2). It’s the first electron indicated by ml=-1