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We can graph out what this is where we're graphing the radial probability density as a function of the radius.
我们可以，画出它来,这是径向概率密度,作为半径的一个函数图。
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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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It's good to have a vector pointing in the radial direction of length one.
所以引入这么一个模长为 1,方向沿圆心向外辐射的矢量作用很大
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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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So if we superimpose our radial probability distribution onto the Bohr radius, we see it's much more complicated than just having a discreet radius.
为波尔半径,这其实比分立的轨道,要复杂很多，我们可以有任何的半径,但有些半径的概率。
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But you should see that there are four radial nodes here since we have a 5 s orbital.
但你们应该知道,这里有４个节点，因为它是５ｓ轨道。
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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, I'm asking very specifically about radial nodes here, how many radial nodes does a hydrogen atom 3 d orbital have?
我问的是径向节点，这里3d轨道的径向节点有多少个？
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OK. So let's actually go to a clicker question now on radial probability distributions.
好，让我们来做一个关于,径向概率分布的题目。
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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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OK. So we should be able to figure this out for any orbital that we're discussing, and when we can figure out especially radial nodes, we have a good head start on going ahead and thinking about drawing radial probability distributions.
我们可以将这种方法,用于任何轨道，当我们可以算出有多少个径向节点的时候，我们就为画出径向概率分布,开了个好头。
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Yup, zero radial nodes. So, for a 2 p orbital, all the nodes actually turn out to be angular nodes.
没有，对于2p轨道，所有的节点都是角向节点。
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So, I think we're a little bit out of time today, but we'll start next class with thinking about drawing radial probability distributions of more than just the 1 s orbital.
快没时间了,但我们，在下节课会讲,1s轨道以外的,径向概率分布。
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At each point, er is a different vector pointing in the radial direction of length one.
矢量 er 在每一点处都不同,方向都从圆心指向该点,模长为1
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So what we're graphing here is the radius as a function of radial probability.
我们要画的是径向概率,作为半径的函数分布。
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So, the example that we took on Monday and that we ended with when we ended class, was looking at the 1 s orbital for hydrogen atom, and what we could do is we could graph the radial probability as a function of radius here.
周一我们,最后讲到了，粒子是氢原子１ｓ轨道，我们可以画出,这幅径向概率分布曲线。
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so when we think about what it is that this radial probability distribution is telling us, it's telling us that it is most likely that an electron in a 2 s orbital of hydrogen is six times further away from the nucleus than it is in a 1 s orbital.
我们来讨论一下这个径向概率分布,告诉了我们什么，它告诉我们,对于氢原子２ｓ轨道的电子,最可能位置是１ｓ轨道的６倍。
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So, this should be pretty straight forward, 100% let's see if we can get close to a 100% on this one, which is how many radial nodes does a 4 p orbital have?
很简单,让我们来看看这题，我们是不是可以接近%,对于一个4p轨道，它有多少个节点？,给你们10秒钟？
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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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