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In an orbital is remember that this area right here at r equals zerio, that is not a node.
例如对于１ｓ轨道,记住这里ｒ等于０处不是一个节点。
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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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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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It's says find the mid-point and split the list in half. Copy of the back end, sorry, copy of the left side, copy of the right side.
找到列表的中间节点,然后在这里将列表分解成两半，后端的拷贝，左部分的拷贝，右部分的拷贝。
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So, by definition, we'll be run by morons pretty soon We're not too far from that right now -from that point in our economic history.
所以理论上说公司很快就被傻子们所掌控了,我国的公司离那一点不远了,-离经济史上那一节点不远了。
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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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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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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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At each node, I'm going to go left until I can't go any further.
在每一个节点，我都会先走左边的分支,直到走不下去。
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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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But what we're saying is there's a node here, so that there's no probability of finding an electron between those two points.
但我们说在节点这里，这两点是,不可能发现电子的。
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So this, where we start at zero is not a node, is the first thing to point out.
零点不是节点，这是第一个要指出来的，当我们。
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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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They're pretty straight forward to do and it gives us an idea what kind of nodal structure we can expect it an orbital.
这个对我们来说很明显,而且让我们对,预计是哪类节点有个概念。
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So what we should expect to see is one radial node, and that is what we see here 3s in the probability density plot.
个节点,这就是我们，在这概率密度图上所看到的,如果我们考虑。
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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 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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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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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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That is to say, I'm going to go back to a node I've already visited.
也就是说我将要,返回我访问过的节点。
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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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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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