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The magnetic quantum number was defined as the number that "labels different orbitals of a subshell" from lecture on Wednesday. The allowed values are l, l-1.....-l If that number is supposed to differentiate particular orbitals, how can it be negative?
For this quantum number, the reason that it can have negative numbers for the orbitals is because it mirrors whatever positive number you get based off what l equals: therefore if you get m= 1, then it can be 1, 0, and -1, and if m=2 then it can be 2, 1, 0, -1, -2.
I also don't exactly know why we have negative numbers and would like to know why. However, I feel that when thinking about the Magnetic Quantum Number, we should pay more attention to how many values there are. For example, in the previous reply it is stated that when m=2, ml= -2,-1,0,+1,+2. In total these are five values, which corresponds to the information we were given about d- orbitals. s- has 1, p- has 3, d- has 5 and, f- has 7.
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