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So, if we hybridize just these three orbitals, what we're going to end up with is our s p 2 hybrid orbitals.
我们会看到现在有3个未配对的电子，可以成键。
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If you want to have an infinitestimally small change, you end up writing dh is dq sub p.
这是对于有限的变化而言的,如果是一个无限小的变化。
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At this point, we have no other choice but to double up before going to the next energy level, 2px so we'll put a second one in the 2 p x.
在这点上我们没有其他选择,而只有双倍填充,在到下一个能级之前，所以我们放入第二个电子至。
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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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px 2py So we need to fill all the way up to the pi 2 p x, and the pi 2 p y.
我们需要填到。
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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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if we move up one of our electrons into an empty p orbital, what were going to see is now we have three unpaired electrons that are ready for bonding.
教授：嗯，如果我们把其中,一个电子填入p轨道。
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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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So, our two glitches we see when we go from the 2 p, or from 2 s to start filling the 2 p, and then we also get another glitch when we've half-filled the 2 p, and now we're adding and having to double up in one of those p orbitals.
因此，我们的看到的两个小偏差，一个是在开始进入，2，p，轨道，或者说在填满，2，s，轨道之后,开始填，2，p，轨道的时候出现的，另一个则是在，2，p，轨道半满之后,开始继续加电子，使得其中一个，p，轨道上的。
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And now we get the p orbitals, remember we want to fill up 1 orbital at a time before we double up, so we'll put one in the 2 p x, then one in the 2 p z, and then one in the 2 p y.
我们到了p轨道，记住在双倍填充之前,我们想要每次填充至一个轨道，所以我们在2px填充一个然后2pz填充一个，然后2py填充一个。
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And if we hybridize these orbitals in carbon, what we end up with is having two hybrid orbitals, and then we're going to be left with two of our p orbitals that are each going to have an electron associated in them.
如果我们杂化碳原子里这些轨道，我们能得到两个杂化轨道，另外剩下两个p轨道,每个里面有一个电子。
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That's equivalent to doing the integral, and so, what we end up getting is that the reversible work v2 pdv is equal to minus integral V1, V2, p dV.
这与刚才的积分过程效果相同，最后，我们得到的结论是可逆过程的功,是负的积分，从v1到。
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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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So essentially, we have two ethene or ethylene molecules here to start with where these blue are our 2 s p 2 hybrid orbitals, so you can see that for each carbon atom, one is already used up binding to another carbon atom.
本质上，我们从两个乙烯分子开始,蓝色的是2sp2杂化轨道，你可以看到，对于每一个碳原子，其中一个已经用来和另外一个碳原子成键。
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But it doesn't actually cost as much energy as you might think, because in this s orbital here we have a paired electron situation where we're moving up to a p orbital where the electron is no longer paired, so it won't feel quite as much electron repulsion, but nonetheless, this is going to cost us energy.
但它消耗的并没有,你们想象的那么多,因为s轨道里我们电子是配对的,当我们把，电子移到p轨道,电子不再配对，所以它不会感受到那么多的电子排斥，但尽管如此，这个过程还是要消耗能量的。
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So if we still have an angle of a 109 . 5 degrees, and again, we still have four unpaired electrons available for bonding, we can make one of those bonds with another s p 3 hybridized carbon, so we're going to make up one pair here.
如果键角仍然是109。,同样，我们还有4个未配对的电子可以用来成键，我们可以用其中的一个,和另外一个sp3杂化碳原子成键，这样我们可以组成一对。
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