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What are the allowed values for each of the four quantum numbers: $n, l, m_{l},$ and $m_{s} ?$

Chemistry 101

Chapter 6

Electronic Structure and Periodic Properties of Elements

Electronic Structure

Periodic Table properties

Drexel University

University of Kentucky

University of Toronto

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Chemistry is the science o…

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What are the possible valu…

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for this problem. We want to know the possible values for each of the four quantum numbers. So to do this, we're just gonna walk straight through the four different types of quantum numbers and talk about what their potential values could be. So starting with N and has a gentle quantum numbers from one really to infinity. That's because and represents the principal concept number, which can more or less be attributed to the overall energy level in question. When you're talking about an electron orbital, the L quantum number, I was going to be able to represent any value from zero to and minus one. And the l quantum number represents the angular momentum. And to put it a little bit more simply, the L value can also be thought upto refer to the shape of the orbital itself. And I'll explain that with a brief example. When we're finished going through each of these, the ML quantum number is the magnetic quantum number, and it represents it could be listed any of the possible values for ml or anything from negative lt l. So once you determine what the L value is anything from negative that value through its positive value, including zero can be a value possible for the ML quantum number. Finally, we have M s, which represents the spin of the electrons. We think about our electron orbital diagrams we can draw those electrons is having an up spin aura down spin. You simply represent that using plus remind us 1/2. So to give a brief example, let's say we were looking at this with respect to a three p orbital. The three in this case represents the principal quantum number. That's the overall energy level. Because it's a P orbital, it's L value is going to be one. That's this standard value given to pee Orbital's because it has no value of one. It's possible ML values are negative 10 and one. And, as is always the case with any electron within these orbital's, the potential spend values are plus or minus 1/2. So one electron, so one electron can have values 310 1/2 and there could be another one that's 310 negative, 1/2 in total. All the different possible combinations of these, uh, values yield six possible combinations, which represent the six potential electrons that could be placed within a P orbital maximum

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