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Stage three means the cancer has spread beyond the middle layers of the colon and most likely into nearby lymph nodes.
VOA: standard.2010.03.18
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And in terms of radial nodes, we have 2 minus 1 minus 0, so what we have is one radial node.
对于径向节点，我们有２减去１减去０,所以有一个径向节点。
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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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You can start from one nucleus and go to the next nucleus, and there are no zero planes, no nodes, nothing.
你可以从一个核出发,看向另一个核，中间没有零平面，没有节点，什么也没有。
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So, it turns out that we have zero nodes that we're dealing with when we're talking about a 3 d orbital.
所以结果是,３ｄ轨道没有节点。
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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 I mentioned you should be able to identify both how many nodes you have and what a graph might look like of different radial probability distributions.
我说过你们要能够辨认,不同的径向概率分布有多少个节点,以及它的图画出来,大概是什么样的。
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Another thing to point out in these two graphs is that we do have nodes, and we figured out last time, we calculated how many nodes we should have in a 2 s orbital.
另外这两张图上要指出的是,我们可以看到节点，上次我们知道，我们算了２ｓ轨道有多少个节点。
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You can go ahead and use that equation, or you could figure it out every time, because if you know the total number of nodes, and you know the angular node number, then you know how many nodes you're going to have left.
你们可以直接用这个方程，或者每次都自己算出来，因为如果你们知道了总的节点数，又知道角向节点数，就知道剩下的节点数是多少。
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And, in fact, these are the only two types of nodes that we're going to be describing, so we can actually calculate both the total number of notes and the number of each type of node we should expect to see in any type of orbital.
事实上，我们只,描述这两种节点，所以我们可以,计算任何轨道中的,总结点数以及各种节点数。
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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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Three. Good, so everyone that recognized that probably got the right answer of three angular nodes here.
三，很好，那么知道这一点的同学,应该都得到了正确结果,也就是三个角向节点。
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But what we find is that we have two radial nodes. All right.
它有两个节点，好,我们可以转回到讲义上了。
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Yup, so one total node, 2 minus 1 is 1, and that means since l is equal to 1, we have one angular nodes, and that leaves us with how many radial nodes?
一个节点，２减去１等于１,因为ｌ等于１,我们有一个角向节点，那剩下径向节点有多少个呢？
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So if we draw the 2 p orbital, what we just figured out was there should be zero radial nodes, so that's what we see here.
如果我们画一个２ｐ轨道，我们刚才知道了是没有径向节点的，我们在这可以看到。
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So we talked about radial nodes when we're doing these radial probability density diagrams here.
我们画这些径向概率分布图的时候,讨论过径向节点。
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Let's look now at a p orbital, so how many total nodes do we have here?
让我们来看看ｐ轨道，它有多少个节点呢？
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All we have to figure out is how many nodes we're dealing with and then we can get the general shape of the graph here.
我们要知道的就是有多少个节点,然后我们就能得到图的大致形状了。
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Remember, we're talking about angular nodes here, so you need to read the question carefully.
要知道，我们这里讨论的是角向节点，大家需要看清题目问的是什么。
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So, that's going to be important later when we get to bonding, but just take note of it now, we have two nodes, or we have two lobes, excuse me, each with a separate phase.
这等到我们之后讲到成键时是非常重要的，现在先要记住，我们有两个节点，不好意思，是两个叶瓣，每个都是不同的相位。
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So here, what I'd like you to do is identify the correct radial probability distribution plot for a 5 s orbital, and also make sure that it matches up with the right number of radial nodes that you would expect.
这里，你们要辨认,哪个是５ｓ轨道的正确概率分布，并且确保它和你们,预期的节点数相符合。
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So, you remember from last time radial nodes are values of r at which the wave function and wave function squared are zero, so the difference is now we're just talking about the angular part of the wave function.
你们记得上次说径向节点在,波函数和波函数的平方,等于零的ｒ的处，现在的区别是我们讨论的是,角向波函数。
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So, we can see in our 1 s orbital, how many nodes do we have?
有多个节点呢？,没有节点，嗯？
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The other thing that we looked at, which I want to stress again and I'll stress it as many times as I can fit it into lecture, because this is something that confuses students when they're trying to identify, for example, different nodes or areas of no probability.
另外一个我们要考虑的事情，我想再强调一次,而且我以后会在课上强调很多次，因为它很容易让人混淆,这就是当你们在确认，节点或者零概率点时候。
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And our equation for total nodes is just the principle quantum number minus 1.
总节点数等于,主量子数减１
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We say there are no nodes, no dropouts, no holidays. No nodes.
相接没有节点，没有空缺，没有假日，没有节点。
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So what I want to point out about them is that they're made up of two nodes, and what you can see is that nodes are shown in different colors here and those are different phases.
关于它们我要指出的是,它们有两个节点，你们可以看到在这里,这些节点的颜色不同，它们的相位不一样。
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So, let me get a little bit more specific about what we mean by nodal plane and where the idea of nodal plane comes from, and nodal planes arise from any place you have angular nodes.
关于节面的意义,或者节面概念的起源，让我们讲的更具体一点，节面起源于角向节点。
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And we talked about the equation you can use for radial nodes last time, and that's just n minus 1 minus l.
我们讲过这个用于,计算径向节点的方程，也就是ｎ减去ｌ减去１
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