(f) Can contain two electrons, both with spin ms = +1/2

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Accepted Answer

Hello everyone today. We are being asked the following question. Among the following sub shells that we have here, which can contain four electrons all with spin quantum numbers abbreviated M sub s equaling negative one half. So for our quantum numbers we have what's known as the principle quantum number or N. And this is simply just our energy level in orbital's and its value can be any positive integer to infinity. Secondly we have our angular momentum quantum number and that is going to be L. And this is just simply going to be in -1. These are sub shells and so L can equal 01, two or 3. If it equals zero we are dealing with an S sub shell if it equals one P. If it equals two we were looking at a D sub shell and if it equals three we're looking at an F sub shell. 3rdly We have our magnetic quantum number or M sub L. And these are simply going to be values ranging from -1 or negative l. Two positive L. And so for example, we're dealing with an S P D. Or F sub shell For s. That could be equal to one p 2. The P orbital would equal three orbital's Our D would equal five orbital's. R. F would have six orbital's N. R s would have just simply one orbital. And it's important to note that one orbital can contain two electrons. So R s orbital can hold a maximum of two electrons P six D. 10 and F can hold a maximum of 14 electrons. And last but not least, we have our spin quantum number abbreviated as m sub S. And this is simply can just be negative 1/2 or positive one half. So it can be one spin up and one spin down, which is what these numbers denote. And so we set up here that each orbital can contain two electrons and thus if we're working with an s orbital. So if we have our one s orbital that can hold a maximum of two electrons. And so if we only We only have one electron with our m sub s equaling negative one half. And that would be the electron that is facing downwards. We're going to jump a little bit, we'll meet with this step five, we'll jump a little bit to the middle of the screen here with our p orbital with our p orbital, we can hold a maximum of six electrons. However, every down arrow represents us having a negative half spin. So we only have three electrons with our sub with our spin, our magnetic spin number or just our spin number being negative one half. We're gonna do the same thing with D, Which has five orbital's as we said before. And so if we draw our electrons out, every down arrow represents a negative half spin. And so D orbital's only have Five electrons with with a spin number of negative 1/2. And just for completion will will draw out our f if we fill in all of these electrons here we see that we have and seven Electrons with a spin number of -1/2. And so we're looking for Among these sub shells which can continue four electrons with their spin quantum number equaling negative 1/2. And so our answer is essentially going to contain only our D orbital's and our F orbital's because our D orbital's can have five and R F orbital can have seven. And so any answer choice that has D and F is going to be correct. This excludes anti choice A. As well as be and see and even E. Which leaves us with the correct answer of D three, D four, D five D four F and five F. And with that we've answered our question overall, I hope that this helped and until next time.

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