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It is an angular glass building with several levels that do not seem to fit together.
VOA: special.2011.04.13
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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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So, first, if I point out when l equals 0, when we have an s orbital, what you see is that angular part of the wave function is equal to a constant.
首先，如果ｌ等于０,那就是ｓ轨道，你们可以看到,它波函数的角度部分是一个常数。
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Bohr expressed the quantum condition by the angular momentum, quantum condition in the following manner.
波尔阐明了他的量子理条件,通过角动量，和以下的量子条件进行量子化。
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You can go ahead and use that equation, or you could figure it out every time, because if you know the total number of nodes, and you know the angular node number, then you know how many nodes you're going to have left.
你们可以直接用这个方程，或者每次都自己算出来，因为如果你们知道了总的节点数，又知道角向节点数，就知道剩下的节点数是多少。
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Angular nodes, we're not going to have any of those, we'll have zero, l equals 0, so we have zero angular nodes.
角向节点，当然,是没有的，０个，ｌ等于０，所以是０个角向节点。
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Yup, so one total node, 2 minus 1 is 1, and that means since l is equal to 1, we have one angular nodes, and that leaves us with how many radial nodes?
一个节点，２减去１等于１,因为ｌ等于１,我们有一个角向节点，那剩下径向节点有多少个呢？
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Three. Good, so everyone that recognized that probably got the right answer of three angular nodes here.
三，很好，那么知道这一点的同学,应该都得到了正确结果,也就是三个角向节点。
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No matter where you specify your electron is in terms of those two angles, it doesn't matter the angular part of your wave function is going to be the same.
不论你将，这两个角度,取成什么值，波函数的角向部分,都是，相同的。
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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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So you can see there's this radial part here, and you have the angular part, you can combine the two parts to get the total wave function.
你们可以看到，这是径向部分，这是角向部分，把这两部分结合到一起,就是总的波函数。
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Remember, we're talking about angular nodes here, so you need to read the question carefully.
要知道，我们这里讨论的是角向节点，大家需要看清题目问的是什么。
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So, you remember from last time radial nodes are values of r at which the wave function and wave function squared are zero, so the difference is now we're just talking about the angular part of the wave function.
你们记得上次说径向节点在,波函数和波函数的平方,等于零的ｒ的处，现在的区别是我们讨论的是,角向波函数。
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Bohr said that the angular momentum, mvr where n is this integer counter h over 2 pi.
波尔提及到角动量，是被量化了的，mvr，is，quantized,这里的n等于一个整数乘以h除以2π
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Bohr says that the energy is quantized through its angular momentum.
波尔说能量通过角动量,被量子化。
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So, let me get a little bit more specific about what we mean by nodal plane and where the idea of nodal plane comes from, and nodal planes arise from any place you have angular nodes.
关于节面的意义,或者节面概念的起源，让我们讲的更具体一点，节面起源于角向节点。
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so, remember we can break up the total wave function into the radial part and the angular part.
记住我们可以把整体波函数,分解成径向部分和角向部分。
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And when we talk about angular nodes, the number of angular nodes we have in an orbital is going to be equal to l.
当我们谈到角向节点时，一个轨道的,角向节点数等于ｌ
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So they do have an angular dependence that we're talking about.
所以它们是随角度变化的。
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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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It describes the angular momentum of the electron.
它描述的是，电子的叫角动量。
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And as a reminder, hopefully I don't need to remind any of you, but exam 1 is on Wednesday, so rather than our clicker question being on something from last class, which is exam 2 material, let's just make sure everyone remembers some small topic from exam 1 material, which is the idea of angular nodes.
而作为一个提醒--我希望大家都不需要提醒，但是这周三就要进行第一次考试了，因此我们的这个选择题,不是关于上节课内容的，那是第二次考试的内容，这里只是想确认大家都记得,第一次考试所要求的一些小问题，也就是关于角向节点的概念。
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I have yet to show you the solution to a wave function for the hydrogen atom, so let me do that here, and then we'll build back up to probability densities, and it turns out that if we're talking about any wave function, we can actually break it up into two components, which are called the radial wave function and angular wave function.
我还没有给你们看过,氢原子波函数的解，让我现在给你们看一下，然后再来说,概率密度，实际上,对于任何一个波函数来说，我们可以把它,分解为两部分，分别叫做径向波函数,和角向波函数。
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And the first is l, and l is angular momentum quantum number, and it's called that because it dictates the angular momentum that our electron has in our atom.
第一个就是l，l是,角动量量子数，叫它这个名字,是因为它表明，原子中,电子的角动量是多少。
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For an angular node, we're just talking about what the l value is, so whatever l is equal to is equal to the number of angular nodes you have.
对于角向节点，我们其实就是在讨论l，的值是多少，因此不管，l，的值等于几,它就等于你所有的角向节点的数目。
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When we look at this angular part, we see that it's always the square root of 1 over 4 pi, it doesn't matter what the angle is, it's not dependent on the angle.
当我们看这角向部分，可以看到它总是等于１除以４pai开根号，这和是什么角度没有关系，它和角度无关。
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So since it's a component of the angular momentum, that means that it's never going to be able to go higher than l is, so it makes sense that, for example, it could start at and then l go all the way up to l.
因为，它是，角动量的分量，这意味着，它不会，比l大，这是很容易理解的，比如说，它可以从零开始,一直到。
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We can actually think about why that is, and the reason is that l is angular momentum.
我们可以这样想，因为，l是角动量。
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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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You can also have angular notes, and when we talk about an anglar node, what we're talking about is values of theta or values of phi at which the wave function, and therefore, the wave function squared, or the probability density are going to be equal to zero.
我们也可以有角向节点，当我们说道一个角向节点时，我们指的是在某个theta的值,或者phi的值的地方，波函数以及波函数的平方，或者概率密度等于零。
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