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And what I want to point out here is this angular dependence for the p orbitals for the l equals 1 orbital.
这里我要指出的是,ｌ等于１的ｐ轨道随角度的变化。
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Sometimes you see this written when you see p orbitals, one is written as plus, one is written in minus.
有时候你们看ｐ轨道时会看到，一个写成正号一个写成负号。
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These are the p orbitals. And, these are what?
这边是P轨道，这些是什么呢？
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And these shapes of p orbitals probably do look familiar to you, most of you, I'm sure, have seen some sort of picture of p orbitals before.
这些ｐ轨道的形状你们可以能已经很熟悉了，我相信大部分人，都看过ｐ轨道的图片。
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It's 109 . 5 is what we would expect for methane because it's tetravalent, but here we're just seeing something that's divalent, and they're both in p orbitals that are perpendicular to each other.
因为甲烷是四价的，我们预测是109。,但这里我们，看到的是二价的，它们都在。
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And it turns out that when you constructively have two p orbitals interfere, and when I say constructively, I mean they're both either positive or they're both the negative lobes, that's when you got bonding.
当两个ｐ轨道,相长干涉时，我说的相干相长，意思就是说它们要么都是,正的叶瓣要么都是负的叶瓣，这时就能成键。
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And so now we can move on to thinking about p orbitals, we now have two ways to talk about p orbitals.
现在我们可以继续来讲ｐ轨道了，我们有两种办法来讨论ｐ轨道。
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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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We'll finish that up, and then we're going to move on to talking about the p orbitals.
我们将会结束这部分讨论，并且继续讨论ｐ轨道。
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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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And the last bond that we have here is a carbon-carbon bond, and this is our last p orbitals that are coming together.
最后一个键是碳碳键，这是最后一个组合的p轨道。
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So again, looking at the shapes, now we're just combining two, we've got these two equal hybrid orbitals plus these 2 p orbitals here.
同样，我们看它的形状，现在我们仅仅结合两个轨道，我们得到这两个杂化轨道,和两个p轨道。
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There's no more 2 p orbitals to put it into, so we're going to actually have to double up.
现在并没有多余的2，p，轨道来放它，我们只能在其中一个，2，p，轨道上放上两个。
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So when we talk about p orbitals, it's similar to talking about s orbitals, and the difference lies, and now we have a different value for l, so l equals 1 for a p orbital, and we know if we have l equal 1, we can have three different total orbitals that have sub-shell of l equalling 1.
当我们考虑ｐ轨道时，这和ｓ轨道的情形和相似，不同之处在于ｌ的值不一样，对于ｐ轨道，ｌ等于１,我们知道如果ｌ等于１,我们有３个,不同的轨道。
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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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So it might look like here, if you don't understand about p orbitals, which I know all you do, but if someone else was just looking and seeing, it kind of looks like there's two bonds here.
这里看起来有点像，如果你们不知道p轨道的话，我知道你们都知道，但如果另外有个人看到这个，这看起来有点像两个键。
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You need to know how to think about them in the same way we think about s and p orbitals, but for example, you don't yet need to know what all of the names are except for this 3 d z squared here.
你们只要知道，如何像考虑s和p轨道一样,来考虑它们，但你们不需要,知道它们的名字,除了这个3dz2轨道外。
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What about this second bond here sigma where we're going to have interaction of 2 p orbitals, is that sigma or pi?
那2p轨道相互作用的第二个键呢,它是，还是π？
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So I changed the colors here to show that these are 2 p orbitals with an opposite phase or an opposite sign.
我这里换了一种颜色,表示2p轨道,不同的相位或者是正负号。
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So again, what we're talking about is the linear combination of atomic 2 p orbitals, and now we're talking about 2 p z.
同样，我们说的是,原子2p轨道的线性组合，现在我们我们说的是2pz。
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Now we're going to start in with that pi 2 p orbitals, which gives us 1 each, and then two each in those, we'll go up to our sigma 2 p z orbital.
现在我们要填π2p轨道，每个1个，然后每个2个，我们我们填sigma2pz轨道。
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And specifically, when we give them a name it's very clear exactly which orbitals they come from combining, - we're calling these s p 3 orbitals -- that's because they come from combining 1 s orbital and 3 p orbitals.
特别的，我们命名它们,使得很容易看到它们是什么轨道结合而成的，我们叫这些轨道sp3轨道-,这是因为它们是由1s轨道,和3p轨道组合成的。
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And the significant difference between s orbitals and p orbitals that comes from the fact that we do have angular momentum here in these p orbitals, is that p orbital wave functions do, in fact, have theta and phi dependence.
轨道和ｐ轨道的,不同之处在于,在ｐ轨道，波函数，随theta和phi变化。
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So if we don't have to hybridize one of the p orbitals, we can actually end up with a lower energy situation, because now these s p 2 orbitals are 1/3 s character, and only 2/3 p character, instead of 3/4.
我们的杂化轨道就有更多的p轨道成分，所以它们的能量更高，如果我们不杂化这个p轨道，我们可以得到一个能量更低的情况。
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When we talk about p orbitals the phase of the orbital becomes important once we talk about bonding, which hopefully you were happy to hear at the beginning of class we will get to soon.
对于ｐ轨道,当我们讨论到成键时，轨道的相位就变得非常重要了,这个我们马上就要讲到了。
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So if we go ahead and hybridize our p orbitals and our s orbitals, we'll switch from having these original orbitals to having something called hybrid orbitals.
如果我们,杂化p轨道和s轨道，我们会从原来的轨道,变成一个叫杂化轨道的东西。
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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 z equals 7 -- this is the cut-off where, in fact, the sigma orbital is going to be higher in energy than the pi 2 p orbitals.
所以z等于7-这是分界点，实际上，sigma轨道能量,要比π2p轨道高。
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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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Would you expect to see electron promotion in nitrogen where we pull one of these 2 s electrons into one of the 2 p orbitals?
你们觉得会看到电子激发吗？,1个2s电子,跑到2p轨道里？
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