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So, actually I want you to go ahead in your notes and circle that zero point and write "not a node."
在你们笔记上把这个零点圈出来,在旁边写上“不是节点“,它不是节点“
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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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5 0 The first node will be the to-pull 2, 5 and 0.
第一个节点是可获取的物品。
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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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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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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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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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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 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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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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And also that we know that the zero does not count as a node, if per se I actually had managed to hit zero in drawing that, so the correct answer would be the bottom one there.
另外你们要知道零点不是节点，假设说我确实把零点画成０了，那正确的结果就是底下这个。
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I'm glad to hear that no one counted this r equal zero as a node.
我很高兴没听到有人把ｒ等于０这处也算作是一个节点。
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And in terms of radial nodes, we expect to see one node.
对于径向节点，应该有１个。
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And what is this node going to look like?
这个节点应该是什么样子呢？
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The point I wanted to make is that for every node, except the leaves, the leaves are the bottom of a tree in this case, are weird, right, they draw trees where the root is at the top, and the leaves are at the bottom.
你没必要看到整棵树，我想说的重点是,对每个节点来说，除了叶子节点,叶子节点指的是树的最下面的节点，电脑科学家都很奇怪,他们画树的时候根是在最上面的。
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So that's why we have this zero point here, and just to point out again and again and again, it's not a radial node, it's just a point where we're starting our graph, because we're multiplying it by r equals zero.
这就是为什么在这里有个零点，我需要再三强调，这不是径向零点，他只是我们画图的起始处，因为我们用ｒ等于０乘以它。
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For an angular node, we're just talking about what the l value is, so whatever l is equal to is equal to the number of angular nodes you have.
对于角向节点，我们其实就是在讨论l，的值是多少，因此不管，l，的值等于几,它就等于你所有的角向节点的数目。
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We'll introduce in the next course angular nodes, but today we're just going to be talking about radial nodes, psi and a radial node is a value for r at which psi, and therefore, 0 also the probability psi squared is going to be equal to zero.
将会介绍角节点,但我们今天讲的是，径向节点，径向节点就是指，对于某个r的值,当然，也包括psi的平方，等于,当我们说到s轨道时。
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