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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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If we're in L.A, where should we go?
如果我们现在在洛杉矶，我们应该去哪儿呢?
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So here we have 3 minus l equals 0, because it's an s orbital, minus 1, so we have two radial nodes here.
这里我们有３减去ｌ等于０,因为这是ｓ轨道，减去１,我们有两个径向节点。
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Let's have a little review of the career of the great poet Orpheus as we get it certainly in L'Allegro and Il Penseroso.
让我们看看伟大诗人俄耳甫斯的经历,这在《快乐的人》和《沉思的人》中都有所提及。
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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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So I'm not even willing to use the L words in describing what it is we have." Right?
甚至不愿意,用爱来表达我们之间的关系？
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Under the L group we've got negative, anxious, unsettled.
组下我们有,消极,焦虑,不安
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Now what do we get if we print l? MIT is gone.
再试试显示数组内容，MIT没了。
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And we can calculate that with the formula that we used, which was just n minus l minus 1 equals the number of nodes.
这个我们可以用我们以前用过的那个公式来计算，也就是节点数等于ｎ减去ｌ减去１
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So chlorine, if we talk about it in terms of electron affinity, we would be writing that we're actually gaining an electron here, and getting the ion, c l minus.
那么，氯，如果我们要讨论它的电子亲和能，我们会假设它真的得到了,一个电子而变成离子，负一价的氯。
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So, you should know that there's four radial nodes, right, we have 5 minus 1 minus l -- is there a question?
你们要记住这里有四个节点，对吧，５减去１减去ｌ，有问题吗？
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Angular nodes, we're not going to have any of those, we'll have zero, l equals 0, so we have zero angular nodes.
角向节点，当然,是没有的，０个，ｌ等于０，所以是０个角向节点。
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So that's why we saw, for example, in the p orbitals we had one angular node in each p orbital, because l is equal to 1 there.
这就是为什么在ｐ轨道中,每个轨道节点数都是１,因为这里ｌ等于１．
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How many bonding electrons does c l have? All right. Let's see, we've got a mixed response here, it turns out it has two bonding electrons.
氯有多少成键电子？好，让我们来看看，大家的回答不太一致，结果应该是两个成键电子。
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And the last example that we're going to talk about is thionyl chloride, so it's s o c l 2. This is another good step forward, because now we actually have four different atoms in our molecule.
我们要讨论的最后一个例子,是氯化亚砜，就是硫，氧，氯，二，这又是一个进步，因为我们的分子中现在有四个不同的原子了。
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R And we abbreviate that by calling it r, l by two quantum numbers, and an l as a function of little r, radius.
我们把它简称为，两个指定的量子数n和，它是半径小r的函数。
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So let's just think exactly what this means, and that means that if we take away function and we define it in terms of n, l and m sub l, what we're defining here is the complete description of an orbital.
让我们来考虑一下这是什么意思，这是说如果我们不考虑波函数,而是用ｎ，ｌ，ｍ下标ｌ来定义它，我们定义的,是一个轨道的完整描述。
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So when we talk about p orbitals, it's similar to talking about s orbitals, and the difference lies, and now we have a different value for l, so l equals 1 for a p orbital, and we know if we have l equal 1, we can have three different total orbitals that have sub-shell of l equalling 1.
当我们考虑ｐ轨道时，这和ｓ轨道的情形和相似，不同之处在于ｌ的值不一样，对于ｐ轨道，ｌ等于１,我们知道如果ｌ等于１,我们有３个,不同的轨道。
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And unlike n, l can start all the way down at 0, and it increases by integer value, so we go 1, 2, 3, and all the way up.
不像n，l可以从0开始取，然后每次增加一个整数，所以我们可以去1，2，3，一直下去。
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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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s We are back over to E as a function of n, l, m and s, only we got there through this other torturous route.
我们回到将E作为函数n，l和，只要我们解决了这个烦人的路径。
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So finally, if we talk about our last example of when n is going to be equal 2, l -1 and then minus 1 for m.
最后我们要讲的,这个例子，是n等于2时，等于1，we，can，have，2，，1，for，l,而m等于。
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ml=-2 So let's say we have n equals 4, and n sub l equalling negative 2.
这里n等于。
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But also unlike n, l cannot have just any value, we can't go into infinity.
但不像n，l，不能取所有整数，不能到正无穷。
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We know that the orbitals for multi-electron atoms depend both on n and on l.
我们知道对于多电子原子轨道,是依赖于n和l的。
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So when we talk about a wave function squared, n l m he wave function, any one that we specify between n, l and m, at any position that we specify based on r, theta, and phi.
一个波函数,的平方时，对特定,特定位置r，theta，phi波函数，取平方,如果我们取平方。
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m And we saw l and m last day.
上节课我们也讲到了l和。
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The other main difference that we're really going to get to today is that in multi-electron atoms, orbital energies depend not just on the shell, which is what we saw before, not just on the value of n, but also on the angular momentum quantum l number. So they also depend on the sub-shell or l.
我们今天要讨论的,另一个很重要的区别就是,在多电子原子中，轨道能力不仅仅依赖于，我们以前看到的外层，不仅仅依赖于n的值，而是与角动量量子数也有关系,所以它们也依赖于亚外层或者。
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In contrast, if we're taking the wave function and describing it in terms of n, l, m sub l, and now also, the spin, what are we describing here?
相反，如果我们考虑一个波函数,然后用ｎ，ｌ，ｍ小标ｌ,还有自旋，我们描述的是什么？
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The violin string extends from x equals zero to x equals L, and we pluck the violin string.
弦从X轴指向原点,让x等于L，然后我们拉直那根弦。
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