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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 the case of the 3 s orbital, that's going to be equal to 11 . 5 times a nought.
对于３ｓ轨道，它等于１１．５ａ０．
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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, the size still for an s orbital is larger than for a d orbital, but what we say is that an s electron can actually penetrate closer to the nucleus.
轨道的尺寸比,ｐ轨道还是要大，但我们说的是ｓ轨道可以,穿透到更接近原子核的地方。
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So, first, if I point out when l equals 0, when we have an s orbital, what you see is that angular part of the wave function is equal to a constant.
首先，如果ｌ等于０,那就是ｓ轨道，你们可以看到,它波函数的角度部分是一个常数。
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Another thing to point out in these two graphs is that we do have nodes, and we figured out last time, we calculated how many nodes we should have in a 2 s orbital.
另外这两张图上要指出的是,我们可以看到节点，上次我们知道，我们算了２ｓ轨道有多少个节点。
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So, if I kind of circle where the probability gets somewhat substantial here, you can see we're much closer to the nucleus at the s orbital than we are for the p, then when we are for the d.
我把概率,很大的地方圈出来，你们可以看到在ｓ轨道上,比ｐ轨道更接近原子核，最远是ｄ轨道。
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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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We talked about the wave function for a 2 s orbital, and also for a 3 s orbital.
我们讲过２ｓ轨道的波函数，也讲过３ｓ轨道。
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And for a 2 s orbital, you get a graph that's going to look something like this.
对于２ｓ轨道，你们可以得到一个大致是这样的图。
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So the most basic answer that doesn't explain why is just to say well, the s orbital is lower in energy than the p orbital, but we now have a more complete answer, so we can actually describe why that is.
所以最基本的答案是那没有解释,所以我们事实上可以描述，为什么是那样，但是我们现在有一个更复杂的答案，又是有效电荷量。
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And it turns out that for a 2 s orbital, that's equal to 6 times a nought.
对于２ｓ轨道，它等于６倍的ａ０
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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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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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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 again, what we're saying here is that it is most likely in the 3 s orbital that we would find the electron 11 and 1/2 times further away from the nucleus than we would in a around state hydrogen atom.
同样我们,这里说的是,氢原子３ｓ轨道中,最可能找到电子的地方,是基态的１１．５倍。
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So, we can see in our 1 s orbital, how many nodes do we have?
有多个节点呢？,没有节点，嗯？
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So we can also look at this in terms of the 3 s orbital.
我们可以同样的来看下３ｓ轨道。
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So we expect to see two nodes right here in the 3 s orbital.
所以在３ｓ轨道中我们预计能看到两个节点。
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And how many nodes do you see in the 3 s orbital?
那３ｓ轨道有多少个节点呢？
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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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So, using the terminology of chemists, which is a good thing to do, because in this course we are all chemists, we want to make sure that we're not using just the physical description of the numbers, but that we can correlate it to 1 0 0 what we understand as orbitals, and instead of 1, 0, 0, 1s we call this the 1 s orbital.
我们最好学会，利用这些化学术语，因为我们这课,就是关于化学的，我们,不仅要知道，这些数字,的物理描述，还要能把它,和我们知道的轨道联系起来，我们叫它。
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When we talk about the n equals 2 state, we now have 2 squared or 4 degenerate same energy orbitals, and those are the 2 s orbital.
当考虑n等于2的态时，我们有2的平方,或者4个简并能量的轨道，它们是2s轨道。
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We got them from combining again, 1 s orbital and the 3 p orbitals. If we hybridize these, what we end up seeing are these four hybrid orbitals.
我们把1s轨道，和3p轨道结合而得到它们，如果我们杂化它们，我们最后会看到4个杂化轨道。
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So it's along the bond axis and it's between a carbon s p 2 hybrid, and then the hydrogen is just a 1 s orbital that we're combining here.
所以它是沿着键轴方向的,而且这里是一个碳sp2杂化轨道，和一个氢的1s轨道的结合,在这里我们可以合并他们。
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H2 So the simplest case we can think of is with h 2 where we have two unpaired electrons, each in a 1 s orbital of a separate h atom.
最容易想到的例子是2,我们有两个未配对电子，每个都在一个分开的1s轨道上。
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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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And if we think about the six hydrogens, now each of those are going to bind by combining one of the carbon hybrid orbitals to a 1 s orbital of hydrogen.
如果我们考虑有六个氢原子，每个都会合起来,碳杂化轨道成键,每个氢的1s轨道。
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So you can see here in this slide we have the atomic orbitals for the two hydrogen atoms, each of them have one electron in them, hydrogen has one electron in a 1 s orbital.
从这个幻灯片你们可以看到我们,有这两个氢原子的原子轨道，每个上面有个电子，氢原子上面有一个电子在1s轨道上。
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And it turns out that if we're talking about a 2 s orbital in an ion, that means it doesn't have as many electrons in it, so what we're going to see is less shielding.
结果是当我们讨论,一个离子中的，2，s，轨道的时候，这意味着里面没有多的电子，那么电子的屏蔽效应会更小。
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