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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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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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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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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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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 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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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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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, 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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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 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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We'll start with talking about the shape, just like we did with the s orbitals, and then move on to those radial probability distributions and compare the radial probability at different radius for p orbital versus an s orbital.
想我们对待ｓ轨道那样，我们先讨论ｐ轨道的形状，然后是径向概率密度分布,并且把ｓ轨道和ｐ轨道在,不同半径处的径向概率做一个比较。
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We'd started on Monday talking about radial probability distributions for the s orbitals.
我们从星期一开始讨论了,ｓ轨道的径向概率分布。
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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, 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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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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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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For example, when we're talking about radial probability distributions, the most probable radius is closer into the nucleus than it is for the s orbital.
举例来说当我们讨论径向概率分布时,距离原子核最可能的半径是，比s轨道半径,更近的可以离原子核有多近。
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But there's also a way to get rid of the volume part and actually talk about the probability of finding an electron at some certain area within the atom, and this is what we do using radial probability distribution graphs.
除去体积部分,来讨论,在某些区域内,发现一个原子的概率,我们可以，用，径向概率分布图,它是。
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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, there are 2 different things that we can compare when we're comparing graphs of radial probability distribution, and the first thing we can do is think about well, how does the radius change, or the most probable radius change when we're increasing n, when we're increasing the principle quantum number here?
当比较这些径向概率分布图,的时候，我们可以比较两个东西，第一个就是考虑当我们增加ｎ,当我们增加主量子数的时候，半径怎么变，最可能半径怎么变化？
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The reason in our radial probability distributions we start -- the reason, if you look at the zero point on the radius that we start at zero is because we're multiplying the probability density by some volume, and when we're not anywhere 0 from the nucleus, that volume is defined as zero.
在径向概率密度里，我们开始,如果你们看半径的零点，我们从零点开始,因为我们用概率密,度乘以体积,而当我们，在离核子很近的地方,体积是，所以我们会在这里。
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