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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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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 yet, we know that the shape of the s orbital is spherical.
并且，我们知道S轨道是球状的。
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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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So if we compare l increasing here, so a 3 s to a 3 p to a 3 d, what we find is that it's only in the s orbital that we have a significant probability of actually getting very close to the nucleus.
我们比较当ｌ变大的时候，从３ｓ到３ｐ到３ｄ,我们可以发现只有ｓ轨道,有很大的概率,非常接近原子核。
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If you compare the s orbital with the bottom lobe, these have a different sign so they're going to destructively interfere.
如果你们比较s轨道和下面这叶，它们正负号相反,所以它们相消干涉。
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The graph to the left, this is the s orbital, symmetric.
在左边的图是对称的S轨道，对称的。
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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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And I am going to superscript it molecular orbital, and this upper one, to indicate that it's antibonding, has the asterisk.
我将给分子轨道加上标，这个上标，表示反键轨道，有一个星号。
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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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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 in s p 2 hybridization, instead of combining all four, we're just combining two of the p orbitals with the s orbital.
这样就能得到sp2杂化，在sp2杂化中，不是四个轨道结合。
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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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Let's switch to a clicker question and just confirm that that is, in fact, true. So what's the corresponding orbital if we talk about this state, 5, 1, 0?
让我们,转到，课堂问题上来，5，1，0态所对应的轨道,是哪一个？
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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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You might have thought before we started talking about molecular orbital theory that non-bonding was the opposite of bonding, it's not, anti-bonding is the opposite of bonding, and anti-bonding is not non-bonding.
你也许在我们讨论分子轨道之前,就想过非成键时成键的反面，它不是，反键才是成键的反面，反键不是非成键。
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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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The electron's going to come out of that highest occupied atomic orbital, that one that's the highest in energy, because that's going to be the at least amount of energy it needs to eject something.
这个电子应该是从,最高的被占据轨道上出来的，它的能级是最高的，因为这样的话发射出它,只需要消耗最少的能量。
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So, let's draw in our electrons there, so we have our two electrons now in the molecular orbital.
让我们把电子画在这里，我们现在有两个电子在分子轨道里。
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Now, from your book as well, this is the pz's of the two atomic orbitals forming the bonding orbital.
现在，也是你们书上，这是两个pz轨道,组成的成键轨道。
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Specifically, we'll talk more about this, it's talking about different orbitals, it's the spatial part of an orbital.
特别地，我们将会谈到它，谈论有关不同轨道的问题，它是一个轨道的空间部分。
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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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So, if we look at the molecular orbital, that's actually going to be lower in energy than either of the two atomic orbitals.
如果我们看分子轨道的话，它实际上要比,两个原子轨道都要低。
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It makes sense that it's going to come out of the highest occupied atomic orbital, because that's going to be the lowest amount of energy that's required to actually eject an electron.
从最高占据轨道上,去掉一个电子是合理的，因为这样是发射一个电子,所损失的最低能量。
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Also, it is cylindrically symmetric around the bonding axis, so this is how we know that it's a sigma orbital.
此外，它关于键轴是圆柱对称的，这就是为什么我们知道它是sigma轨道。
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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, our first orbital that an electron 1 s must be coming from is the 1 s.
所以，我们的第一个肯定有电子,被打出的轨道是。
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So that's why we saw, for example, in the p orbitals we had one angular node in each p orbital, because l is equal to 1 there.
这就是为什么在ｐ轨道中,每个轨道节点数都是１,因为这里ｌ等于１．
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It's the same thing with molecules a molecular wave function just means a molecular orbital.
这对于分子也是一样,分子波函数就意味着分子轨道。
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So the probability again, that's just the orbital squared, the wave function squared.
同样，概率密度，这就是轨道的平方，波函数的平方。
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