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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, let's go ahead and think about drawing what that would look like in terms of the radial probability distribution.
让我们来想一想如果把它的,径向概率分布画出来是怎么样的。
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The field is radial.
场是散射状的。
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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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This is the radial probability distribution formula for an s orbital, which is, of course, dealing with something that's spherically symmetrical.
这个ｓ轨道的,径向概率分布公式，它对于球对称,的情形成立。
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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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We will always have r equals zero in these radial probability distribution graphs, and we can think about why that is.
在这些径向概率分布图里,总有ｒ等于０处，我们可以考虑为什么会这样。
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We can talk about the wave function squared, the probability density, or we can talk about the radial probability distribution.
我们可以讨论它,波函数的平方，概率密度，或者可以考虑它的径向概率分布。
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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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Similarly, if we were to look at the radial probability distributions, what we would find is that there's an identical nodal structure.
相似地如果我们看看,径向概率分布,我们会发现有一个完全相同的波节结构。
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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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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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And so, the radial probability density at the nucleus is going to be zero, even though we know the probability density at the nucleus is very high, that's actually where is the highest.
所以径向概率密度,在核子处等于零，虽然我们知道在，核子处概率密度很大,实际上在这里是最大的，这是因为。
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So, let's actually compare the radial probability distribution of p orbitals to what we've already looked at, which are s orbitals, and we'll find that we can get some information out of comparing these graphs.
让我们来比较一下ｐ轨道,和我们看过的,ｓ轨道的径向概率分布，我们发现我们可以通过,比较这些图得到一些信息。
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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 you can see there's this radial part here, and you have the angular part, you can combine the two parts to get the total wave function.
你们可以看到，这是径向部分，这是角向部分，把这两部分结合到一起,就是总的波函数。
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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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I have yet to show you the solution to a wave function for the hydrogen atom, so let me do that here, and then we'll build back up to probability densities, and it turns out that if we're talking about any wave function, we can actually break it up into two components, which are called the radial wave function and angular wave function.
我还没有给你们看过,氢原子波函数的解，让我现在给你们看一下，然后再来说,概率密度，实际上,对于任何一个波函数来说，我们可以把它,分解为两部分，分别叫做径向波函数,和角向波函数。
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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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So, it's very easy to calculate, however, the number of radial nodes, and this works not just for s orbitals, but also for p orbitals, or d orbitals, or whatever kind of work of orbitals you want to discuss.
径向节点，的数量，这不仅对s轨道适用，对p轨道，d轨道，或者任何你们想讨论的轨道，都是适用的,它就等于。
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But still, when we're talking about the radial probability distribution, what we actually want to think about is what's the probability of finding the electron in that shell?
但当我们讲到径向概率分布时,我们想做的是考虑，在某一个壳层里,找到电子的概率,就把它想成是蛋壳？
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It's somewhat different when we're talking about the p or the d orbitals, and we won't go into the equation there, but this will give you an idea of what we're really talking about with this radial probability distribution.
当我们讨论ｐ轨道或者,ｄ轨道的时候会有些不同，我们那时不会给出方程，但它会给你们一个,关于径向概率,分布的概念。
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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 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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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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And in doing that, we'll also talk about the shapes of h atom wave functions, specifically the shapes of orbitals, and then radial probability distribution, which will make sense when we get to it.
为了这样做，我们要讲一讲，氢原子，波函数的形状，特别是轨道的形状，然后要讲到径向概率分布，当我们讲到它时，你们更能理解。
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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, basically what we're saying is if we take any shell that's at some distance away from the nucleus, we can think about what the probability is of finding an electron at that radius, and that's the definition we gave to the radial probability distribution.
本质上我们说的就是,如果我们在距离原子核,某处取一个壳层，我们可以考虑在这个半径处,发现电子的概率，这就是我们给出的,径向概率密度的定义。
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