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And Pauli says no two electrons in a given system can have the entire set of quantum numbers identical.
而泡利认为在一个给定的系统内,没有两个电子有完全相同的量子数。
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So by parallel we mean - they're either both spin up remember that's our spin quantum number, that fourth quantum number.
所以我们意味着,它们都是自旋向上,记住我们的自旋量子数，是第四个量子数。
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He has two electrons here with the same set of quantum numbers. B but these are two separate hydrogen atoms.
因为我写了两个量子数,一样的电子,但这是在两个不同原子中啊。
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And this spin magnetic quantum number we abbreviate as m sub s, so that's to differentiate from m sub l.
这个自旋磁量子数我们把它简写成ｍ下标ｓ,以和ｍ小标ｌ有所区分。
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what three quantum numbers tell us, versus what the fourth quantum number can fill in for us in terms of information.
三个量子数和,四个量子数告诉我们的信息。
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OK, great. So, most of you recognize that there are four different possibilities of there's four different electrons that can have those two quantum numbers.
Ｋ，大部分都认为,有４个不同的可能,有四个不同的电子可以有,这两个量子数。
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The other thing that we took note as is what happens as l increases, and specifically as l increases for any given the principle quantum number.
另外一个我们要注意的是,ｌ增加时如何变化，特别是对于某个给定的,主量子数ｌ变化时如何变化。
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So, what we can do instead of talking about the ionization energy, z because that's one of our known quantities, so that we can find z effective.
我们做的事可以代替讨论电离能,因为那是我们知道的量子数之一，那是我们可以解出有效的，如果我们重新排列这个方程。
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So we can have, if we have the final quantum number m equal plus 1 or minus 1, we're dealing with a p x or a p y orbital.
所以如果我们有,磁量子数ｍ等于正负１,我们讨论的就是ｐｘ或者ｐｙ轨道。
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And when you solved the relativistic form of the Schrodinger equation, what you end up with is that you can have two possible values for the magnetic spin quantum number.
当你们解相对论形式的,薛定谔方程，你们最后会得到两个,可能的自旋磁量子数的值。
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So if we're talking about the fourth excited state, and we talk instead about principle quantum numbers, what principle quantum number corresponds to the fourth excited state of a hydrogen atom.
如果我们说的是,第四激发态，我们用,主量子数来描述，哪个主量子数对应了,氢原子的第四激发态？
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All right. So let's look at some of these wave functions and make sure that we know how to name all of them in terms of orbitals and not just in terms of their numbers.
好，让我们来看一下,这些波函数,并确定我们都知道,怎么用轨道,而不仅是量子数来命名它们,一旦我们可以命名它们。
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So let's go to a second clicker question here and try one more. So why don't you tell me how many possible orbitals you can have in a single atom that have the following two quantum numbers?
让我们来看下一道题目,你们来告诉我,有多少个可能的轨道,含有这些量子数呢？
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We didn't just need that n, not just the principle quantum number that we needed to discuss the energy, but we also need to talk about l and m, as we did in our clicker question up here.
我们不仅需要ｎ,不仅要这个可以,决定能量的主量子数，还需要ｍ和ｌ,就像我们做这道题这样。
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Yeah. So we have two orbitals, or four electrons that can have that set of quantum numbers.
嗯，有我们有两个轨道，也就是４个电子可以有这套量子数。
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So if we think about, for example, this red line here, which energy state or which principle quantum number do you think that our electron started in?
我们来看看，比如这里的这个红线，它是从主量子数,等于多少的能级发出的？
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No, we can't. Because if l equals 1, we can not have m sub l equal negative 2, right, because the magnetic quantum number only goes from negative l to positive l here.
不行，因为如果ｌ等于１,ｍｌ的值不可能等于－２，对吧，因为磁量子数的值,这时只能从－１到１
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So there's two different orbitals that can have these three quantum numbers, but if we're talking about electrons, we can also talk about m sub s, so if we have two orbitals, how many electrons can we have total?
所以有两个轨道可以有,这三个量子数，但如果我们讲的是电子，我们还要考虑ｍ小标ｓ,如果我们有两个轨道，一共有多少个电子呢？
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All right, so hopefully if you see any other combination of quantum numbers, for example, if it doesn't quickly come to you how many orbitals you have, you can actually try to write out all the possible orbitals and that should get you started.
所以希望你们如果遇到,任何其它的量子数组合的问题，如果你们不能马上想到有多少个轨道，可以试着先写出所有的轨道,这是个不错的切入点。
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n l m s Once we have chosen a certain mix of n, l, m and s, it is used once for that particular atom.
一旦我们选定了一组量子数，它就只能被一个固定原子所有。
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But at the time, they didn't have a well-formed name for it, they were just saying OK, there's this fourth quantum number, there's this intrinsic property in the electron.
但在那时，人们没有给它取名，他们只是说ｏｋ，这是第四个量子数，这是电子的本征性质，
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So now we're just counting up our orbitals, an orbital is completely described by the 3 quantum numbers.
所以现在我们只要把这些轨道加起来，一个轨道是由３个量子数完全确定的。
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1/2 And we have the spin quantum number 2 as plus 1/2 for electron one, -1/2 and minus 1/2 for the electron two.
我们有自旋量子数,对于电子，我们有自旋量子数。
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So each electron has a distinct set of quantum numbers, the first important idea.
每个电子的量子数,是不尽不同的，对于这第一个重要观点。
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- The same place is that energy is a function of these four quantum numbers.
它就是这个结论,能量是这四个量子数的机能显示。
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The reason there are three quantum numbers is we're describing an orbital in three dimensions, so it makes sense that we would need to describe in terms of three different quantum numbers.
我们需要，3个量子数的原因,是因为我们描述的是一个，三维的轨道，所以我们需要，3个不同的量子数,来描述它。
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So, there's two kind of cartoons shown here that give you a little bit of an idea of what this quantum number tells us.
这里展示的两个图片,可以让你们对,这个量子数有些概念。
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So, we need to actually add on this fourth quantum number, 1/2 and it's either going to be plus 1/2 or negative 1/2.
所以我们需要加上这第四个量子数，它等于1/2或者负的。
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So you'll notice in your problem-set, sometimes you're asked for a number of orbitals with a set of quantum numbers, sometimes you're asked for a number of electrons for a set of quantum numbers.
希望你们在做习题的时候注意到，有时候问的是拥有,一套量子数的轨道数，有时候问的是拥有一套,量子数的电子数。
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And I just want to point out that now we have these three quantum numbers.
我想指出的是,现在我们有了，这3个量子数。
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