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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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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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And so, if we look at our box notation, we've got three states in the p orbital.
因此，如果我们看看我们的盒子符号，在p轨道有三个状态。
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And in terms of thinking about the phase of this p orbital, the phase is going to be positive anywhere where z is positive.
对于ｐ轨道的相位，在ｚ大于零的地方都是正的。
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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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So, we end up with a total of six electrons that are possible that have that 2 p orbital value.
所以我们最后,总共得到了6个电子,在所有可能的“2p“轨道值中。
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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 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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Let's look now at a p orbital, so how many total nodes do we have here?
让我们来看看ｐ轨道，它有多少个节点呢？
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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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Yup, zero radial nodes. So, for a 2 p orbital, all the nodes actually turn out to be angular nodes.
没有，对于2p轨道，所有的节点都是角向节点。
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So, if we say that in this entire plane we have zero probability of finding a p electron anywhere in the plane, the plane goes directly through the nucleus in every case but a p orbital, so what we can also say is that there is zero probability of finding a p electron at the nucleus.
而只要是ｐ轨道,这个平面都直接，穿过原子核，那么我们,可以说在原子核上,找到一个ｐ电子的概率为零。
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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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But unlike the case with boron where we had an empty p orbital, we're actually going to have an electron in the p orbital of carbon as well.
但和硼里面有个空的p轨道不同，我们实际上有一个电子,在碳里p轨道里也有电子。
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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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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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So we can also show them coming together this way, so now you're looking at it where you can see the p orbital, and maybe just see well one of the hydrogen atoms.
我们也可以看到它们从这个方向靠拢，现在你看的方向你可以看到p轨道，也许可以看到一个氢原子。
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So we can think about what is our most loosely-bound electron, what's that highest energy orbital, and it's going to be the 2 p orbital, that's going to be what's highest in energy.
我们来想一想,它“束缚得最松“的电子是哪一个，能量最高的轨道是哪一个？,它就是，2，p，轨道，是能量最高的轨道。
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So, this should be pretty straight forward, 100% let's see if we can get close to a 100% on this one, which is how many radial nodes does a 4 p orbital have?
很简单,让我们来看看这题，我们是不是可以接近%,对于一个4p轨道，它有多少个节点？,给你们10秒钟？
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So, for example, for boron, 2s2 now we're dealing with 1 s 2, then 2 s 2, and now we have to move into the p orbital 2p1 so we go to 2 p 1.
举例来说对于硼，现在我们知道有1s2然后，现在我们必须,移至p轨道即。
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So for example, if you know how to draw an s orbital for a hydrogen atom, then you already know how to draw the shape of an s orbital or a p orbital for argon.
举个例子，如果你们知道如果画,氢原子的s轨道，那么你们已经知道如何去,画氩的s轨道和p轨道的形状。
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The other thing that I want you to notice, is if you look at the most probable radius, for the 2 s orbital it's actually out further away from the nucleus than it is for the 2 p orbital.
另外一个你们要注意的地方就是，如果你们看它的最可能半径，2s轨道比2p轨道的,要更加远离原子核。
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Remember we have to put one in each degenerate orbital before we double up on any orbital, so just keep that rule in mind that we would fill one in each p orbital before we a to the second one.
我们必须把,每一个放入简并的轨道,我们把每一个电子放在p轨道里，所以把规则记在脑子里,我们把每一个电子放在p轨道里,在我们放入第二个电子之前。
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So in other words a very low energy is what we're going to have when we talk about the orbitals -- the energy of the 2 s orbital is going to be less than the energy of the 2 p orbital.
换句话说一个非常低的能量,是我们将会得到的当我们谈论轨道时,2s轨道的,能量比2p轨道,的能量低。
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So this is a little bit trickier to look at and see what it means, but essentially we have two hybrid orbitals, which are shown in blue here, and then we have one p orbital that's left alone that's going up and down on the page.
看这个图肯能会觉得比较诡异，但本质上，骂我们有两个杂化轨道，这里用蓝色表示，还有剩下一个p轨道,在图中上下方向上。
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And hybrid orbitals are all going to be completely equal, and lower in energy than the p orbital.
杂化轨道是完全相等的，你会注意到它们的能量比s轨道高，比p轨道低。
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Again, the name is very straightforward, it comes from 1 s and 2 p orbital, so it will be s p 2.
所以，如果我们杂化这三个轨道，我们最后会得到的是sp2杂化轨道，同样，这个名字是很直接的。
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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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What we're proposing here is that you take a nice low energy s electron and move it into a higher energy p orbital.
我们这里说的是,你把一个低能s电子,移到高能p轨道里去。
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