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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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It could form in any direction because the Coulombic field is radial in all directions.
能够在任何方向形成,因为库仑产在全方位发生分散。
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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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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 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 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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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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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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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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So, you should be able to generally identify and draw the general form of these radial probability distributions.
所以你们应该可以大概辨认,并且画出概率,分布的大致形式。
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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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Or we could just look at the radial probability distribution itself and see how many nodes there are.
或者我们可以直接,看径向概率分布图,本身看看里面有几个节点。
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so, remember we can break up the total wave function into the radial part and the angular part.
记住我们可以把整体波函数,分解成径向部分和角向部分。
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So, we can look at other radial probability distributions of other wave functions that we talked about.
我们可以来看一看我们讨论过的,其它一些波函数的径向概率分布。
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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, what you find with the s orbital, and this is general for all s orbitals is that all of your nodes end up being radial nodes.
对于ｓ轨道，你们会发现,所有的节点都是径向节点。
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