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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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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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b The repulsive term goes as some constant lower case b divided by R to the n. N is not the quantum number.
这种斥力很想一个固定的小写字母,被R到n分开的话，N不是量子数。
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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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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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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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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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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, 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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I think this is taken about two years after they discovered the fourth quantum number.
这张照片拍摄于他们发现,第四个量子数的两年后。
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But now, it has come to light that they are the ones that do get credit for first really coming up with this idea of a spin quantum number, and it's interesting to think about how the politics work in different discoveries, as well as the discoveries themselves.
但现在我们,知道他们是,最先想出自旋量子数,这个概念的人，看各种发现中的,政治学是十分有趣的，和发现本身一样有趣。
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s Because the fourth quantum number is s.
因为第四量子数是。
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So we can completely describe an orbital with just using three quantum numbers, but we have this fourth quantum number that describes something about the electron that's required for now a complete description of the electron, and that's the idea of spin.
所以我们可以用３个,量子数完全刻画轨道，但我们有这第四个量子数,来完整的,描述电子，这就是自旋的概念。
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You know from the m quantum number there are three.
你可以从角量子数上看出是3个。
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So, that's the second quantum number.
这就是第二个量子数。
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So, it turns out that n is not the only quantum number needed to describe a wave function, however. There's two more you can see come out of it.
事实上，n不是描述一个波函数需要的,唯一的量子数，你们可以看到，还需要，两个量子数。
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And the first is l, and l is angular momentum quantum number, and it's called that because it dictates the angular momentum that our electron has in our atom.
第一个就是l，l是,角动量量子数，叫它这个名字,是因为它表明，原子中,电子的角动量是多少。
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And when we talk about l it is a quantum number, so because it's a quantum number, we know that it can only have discreet values, it can't just be any value we want, it's very specific values.
当我们讲，l是一个量子数时，因为它是量子数，我们知道，它只能去分立的值，它不能取到所有的数，它取一些确定的数。
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And that's just to take 1 the principle quantum number l and subtract it by 1, and then also subtract from that your l quantum number.
主量子数,减去,再减去，量子数,你们可以对1s轨道来验证一下。
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psi So we're going to for psi, and before that, we're going to figure out that instead of n just that one quantum number n, we're going to have a few other quantum numbers that fall out of solving the Schrodinger equation for what psi is.
我们要讲到，但在这之前，我们已经知道了,主量子数，现在我们需要知道，其他一些,解psi的薛定谔方程,所需要的量子数。
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Core electrons are all those electrons held in really tight with the nucleus in the inner shells, whereas the valence electrons are only those electrons that are in the outer-most shell, or at your highest value of n of the principal quantum number.
芯电子是那些,在内壳层被原子核束缚得非常紧的电子，而价电子只包括,最外层的电子，或者说主量子数，n，的值最大的那些电子。
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Specify the quantum number n and divide by Z.
只需说明n的具体值，并用Z去除就行了。
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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 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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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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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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And I promise, this is the last quantum number that we'll be introducing.
我向你们保证，这是我们最后遇到的一个量子数。
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