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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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OK, in fact if we look at this, if I say, print of p, it prints it out in that form.
好，实际上如果，我们来看看这个，如果我输入，p的显示。
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py And finally, we can look at the 2 p y, so the highest probability is going to be along the y-axis.
最后我们来看一下，概率密度最高的是沿着ｙ轴。
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People make really stupid decisions and so as you know in this course with P sets there are three axes that we look at when evaluating your code.
人们做了一个愚蠢的决定,在这个课程上，通过习题集，当执行你的代码的时候,有三个评估方面。
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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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We might say, look, while you're asleep, it's true that you're not P-functioning.
我们可以说，看，当你睡着时，确实没有人格功能性。
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And it's more dramatic if the system is a gas p T2 V2 p, T2, V2, And let's look at what happens to U these functions of state, to H to u under this transformation.
如果是气体这个系统,就更具有趣了,让我们看看H和，在这个变化中态函数会发生什么变化。
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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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All right. So let's look now at the case where we do have 2 p z orbitals that we're talking about.
好的，让我们现在看一个,需要2pz轨道的例子。
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Well, that's at least an improvement, because then we say, look, while you're asleep, even though there's no P-functioning going on, the lack of P-functioning is temporary, so you're still alive.
这至少算是个改进，因为我们能说，看，你睡着了，即便没有任何人格功能性发生，人格功能性的缺少是暂时的，就说明你还活着。
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OK, and if I wanted to look at it, we can come back over here, and we can see what does c p 1 look like, interesting.
现在对于这里的每个实例，我都赋了x和y值，好，那么如果我想要研究下它,我们可以回到这里来。
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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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So now let's look at an example where we talk about using these 2 p z orbitals, so let's look at oxygen.
现在让我们来看一个要,用到2pz轨道的例子，让我们来看一下氧。
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So let's take a look at another case where we have s p 2 hybridization, we can actually also have it happen in carbon.
它是B2sp2杂化轨道,和H1s轨道的相互作用，让我们看看另外一个。
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So we want to look at any element that has a 3 p orbital filled, but that does not then go on and have a 4 s, because if it had the 4 s filled then we would actually see six lines in the spectrum.
所以，我们要找一找有哪些元素的,3，p，轨道被占据，但没有，4，s，轨道被占据,因为如果，4，s，轨道也被占据了,那我们会在光谱中看到第六条谱线。
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We can look at the 2 p, which should have one radial node, and we just figured it out for the, excuse me, 3d for the 3 p has one radial node, and for the 3 d here, we should have zero radial nodes, we just calculated that.
我们看2p，它有一个节点，我们已经知道对于，不好意思，是3p有一个节点，对于，它应该没有径向节点，我们刚刚算过这个。
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What do these look like? These are p-orbitals.
这看起来像什么，是p轨道。
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So let's look at the first case 2px where we have either the 2 p x or 2 p y type of orbitals that we're combining.
让我们看看第一个情形,我们要组合,或者2py轨道。
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So what we can say is look at each of these separately, so if we start with looking at the 2 p z orbital, the highest probability of finding an electron in the 2 p z orbital, is going to be along this z-axis.
我们可以来分别看看这些图，首先来看看2pz轨道，在2pz轨道里,找到电子的最大概率，是沿着ｚ轴。
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In contrast when we're looking at a p orbital, so any time l is equal to 1, and you look at angular part of the wave function here, what you see is the wave function either depends on theta or is dependent on both theta and phi.
相反当我们看ｐ轨道时，任何时候ｌ等于１,你们看它的角向波函数，你们可以看到它要么是和theta有关,要么是和theta和phi都有关。
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