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You can start from one nucleus and go to the next nucleus, and there are no zero planes, no nodes, nothing.
你可以从一个核出发,看向另一个核，中间没有零平面，没有节点，什么也没有。
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I got my first bachelor's in Graphic Design
我的第一个学士学位是平面设计，
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So what we'll have here is a trigonal planar case, and you can see that we only have three electrons that are set for bonding, so we'll add three hydrogens, and for b h 3, we'll get a stable structure here.
让电子劲量远离的时候，不用考虑它,这个例子是平面三角形，你可以看到，只有3个电子可以成键。
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So an easy thing to do in planar geometry is I want to make a line segment.
在平面几何里比较容易的一件事,就是做一个线段。
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And then I could put a flat end here and I could put phosphorus here.
然后我把一个末端平面放在这儿,一块磷放在这儿。
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Then, I gave you one other very important example of a particle moving in the x-y plane.
下面我再拿一个重要的例子,质点在 x-y 平面内的运动
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I played around a lot with Photoshop and took some classes doing that and I had a...
我经常玩Photoshop（图像处理、平面设计），还上了些这方面的课，我就有……
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And to do that, we're doing this taco truck thing and we're also purchasing Facebook ads and Google ads and doing the standard thing and looking into print media and the Union of Accountants because they might be influencers and their trade magazines.
为了做到这个，我们要做这个塔克卡车的东西并且,我们要购买Facebook的广告,和谷歌的广告，然后让它们标准化,在平面媒体和,会计联合会中寻找机会因为,它们很可能成为影响因素，他们的贸易杂志也很有影响力。
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So here's the example I'm going to start with.
做二维几何的程序,关于平面上的点。
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And when we look at this, it's actually split by what's called a nodal plane, which is pointed out in light orange here on this picture, but what we just mean is that there is this whole plane that separates the two lobes where there is absolutely no electron density.
我们来看这里，实际上它被一个节面分开，在这图里用淡黄色表示，这意味着这个分开,两个叶瓣的平面上,是完全没有电子密度的。
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And that zero point is the node.
这个零平面就是节点。
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Let us say P for plane, G for ground, O for object.
我们定义 P 是平面,G 是地面,O 是物体
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And so it has what? In contrast to the sigma, it has a nodal plane containing both nuclei.
这是什么，和sigma相反，它是包覆在核上的平面电子云，有一个界面。
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So, the wave function at all of these points in this plane is equal to zero, so therefore, also the wave function squared is going to be equal to zero.
因此这里的,波函数平方也等于零，如果我们说在这整个平面上,任何地方找到一个ｐ电子的概率都是零。
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Our picture now is going to be some particle that's traveling in the x-y plane.
我们现在的情景是在 x-y 平面内,运动的质点
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So if you picture, for example, b h 3, it's going to look like this.
如何使键劲量相互远离，我们会有平面三角形的情形，如果你想象。
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So, it's the x-y plane, you can see there's no electron density anywhere there.
它在ｘｙ平面，你们可以看到在这里没有电子密度。
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So again, if we think about that shape of that carbon atom, it's going to be trigonal planar, 120° it's going to have bond angles of 120 degrees, because we have this set up of having three hybrid orbitals.
如果我们考虑碳原子的形状，它是平面三角形，键角是，因为我们有这三个杂化轨道。
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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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And similarly, actually, if we're looking at our polar coordinates here, what we see is it's any place where theta is equal to is what's going to put up on the x-y plane.
类似的，如果我们,看这里的极坐标系，我们能看到只要在theta等于,多少的地方就是ｘｙ平面。
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Um-hmm. So, it's going to be the y z nodal plane, or in other words, we can say it's any place where phi is equal to 90 degrees.
嗯，是ｙｚ平面，换句话说，是在phi等于９０度的面。
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But in sigma orbitals, you have no nodal planes along the bond axis, so if we had a nodal plane here, we'd see an area where the wave function was equal to zero.
但在sigma轨道里，沿着轴向是没有节点平面的，如果我们有个节点，我们就会看到某个地方波函数等于0。
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Another way to represent a point in a plane is I've got a radius and I've got an angle from the x-axis, right, and that's a standard thing you might do.
平面上面的点的方法,也就是极坐标,上面那种方法其实是，如果你们喜欢我这么说的话,笛卡尔坐标表示法。
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Here, we are not talking about a single number, but a displacement in the plane.
我们现在不是在讨论数字,而是平面上的位移
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And the nodal plane's going to be in the x z plane, or again, anywhere where phi is going to be equal to 0, that takes us to the x z plane.
节面是ｘｚ平面，又或者说是phi等于０的地方，这就是ｘｚ面。
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They took a crystal, this is a single crystal of nickel that has regular planes of atoms, and those planes are spaced on the order of an angstrom or less apart, and they irradiated this with x-rays.
他们取了个晶体,一个具有规则原子平面的，镍晶体,这些面间距差不多也是一埃或者更少，它们放射出X射线。
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And in the plane there is some other object.
在平面上有一个物体
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That's the plane with some origin here.
这是一个平面,这里是原点
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Particle's moving in a plane.
物体在平面内运动
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You go back to the same x-y plane; here is some vector A.
回到刚才的 x-y 平面上,这是某个矢量 A
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