History homework help
History homework help. ##l = 0, 1, 2, 3##.
##m_l = -3, -2, -1, 0, 1, 2, 3##
##m_s = +1/2## or ##-1/2##
I assume that you’re talking about the .
So, if you’re not familiar with the concepts behind quantum numbers, I’d recommend you take a look at this video first. If you’re good, let’s go…
So to quickly recap here’s what each quantum number describes:
##n## = energy level.
##l## = subshell; ranges from 0 up to ##n-1##
##m_l## = orbital; ranges from ##-l## to ##l##
##m_s## = tells the spin of the electron; is either ##+1/2## or ##-1/2##
Now, your question asks what are the possible values for ##l##, ##m_l##, and ##m_s## for ##n = 4##. So, let’s just work through this from top to bottom.
Firstly, if ##n=4##, let’s consider what ##l## could be. We know that ##l## ranges between 0 to ##n-1##. Therefore, we can say that:
##l = 0, 1, 2, 3##.
Side note: this essentially means that the n=4 energy level can hold electrons in the s, p, d and f subshells
Okay, so now that we know all possible values of ##l##, let’s look at ##m_l##. We know that ##m_l## ranges between ##-l## and ##l##. But which of the above ##l##’s do we use? Well, consider this: if we just looked at the highest value of ##l## present, it would take care of all the lower ones. See what I mean below:
##m_l = -3, -2, -1, 0, 1, 2, 3##
See how values like ##-2## and ##1## are taken care of?
So, that’s really it. ##m_s## will only be either ##+1/2## or ##-1/2## regardless of the other 3 quantum numbers.
Hope that helped 🙂
