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And when we define that as r being equal to zero, essentially we're multiplying the probability density by zero.
当我们定义ｒ等于０处，事实上是把概率密度乘以０．
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RT2 So it's R T2, right, now we're at a lower temperature times log the log of V4 over V3.
等于，这时温度比刚才低,乘以。
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We're saying the probability of from the nucleus in some very thin shell that we describe by d r.
某一非常薄的壳层dr内,一个原子的概率,你想一个壳层时。
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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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So that's why we have this zero point here, and just to point out again and again and again, it's not a radial node, it's just a point where we're starting our graph, because we're multiplying it by r equals zero.
这就是为什么在这里有个零点，我需要再三强调，这不是径向零点，他只是我们画图的起始处，因为我们用ｒ等于０乘以它。
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So if we take this term, which is a volume term, and multiply it by probability over volume, what we're going to end up with is an actual probability of finding our electron at that distance, r, from the nucleus.
如果我们取这项，也就是体积项然后，乘以概率除以体积，我们能得到的就是真正在距离,原子核ｒ处找到电子的概率。
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So instead of being equal to negative z squared, now we're equal to negative z effective squared times r h all over n squared.
这里不再等于-z的平方，现在我们等于-有效的z的平方,乘以RH除以n的平方。
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R They're related through the gas constant.
理想气体常数。
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So, what we can do to actually get a probability instead of a probability density that we're talking about is to take the wave function squared, which we know is probability density, and multiply it by the volume of that very, very thin spherical shell that we're talking about at distance r.
我们能得到一个概率,而不是概率密度的方法,就是取波函数的平方，也就是概率密度，然后把它乘以一个在ｒ处的,非常非常小的,壳层体积。
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It's kind of ironic that we put this in the same lecture as we talk about atomic radii, which we also call r, but they're two different r's, so you need to keep them separated in terms of what you're talking about.
有点讽刺的是,我们在同一堂课里还讨论过了原子半径，它也是用，r，表示的，但是它们具有不同的意义，因此大家需要注意区分它们,弄清楚我们讨论的是哪一个。
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When we're talking about r for internuclear distance, we're talking about the distance between two different nuclei in a bond, in a covalent bond.
当我们说，r，代表的是核间距的时候，我们讨论的是一个距离,在一个键--一个共价键的两端的原子核之间的距离。
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So we know that we can relate to z effective to the actual energy level of each of those orbitals, and we can do that using this equation here where it's negative z effective squared r h over n squared, we're going to see that again and again.
我们知道我们可以将有效电荷量与,每个轨道的实际能级联系起来，我们可以使用方程去解它,乘以RH除以n的平方,它等于负的有效电荷量的平方,我们将会一次又一次的看到它。
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That should make sense, right, because they're only dependent on r.
这很好理解，对吧，因为它们只和r有关。
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Then we go negative and we go through zero again, which correlates to the second area of zero, that shows up also in our probability density plot, and then we're positive again 0 and approach zero as we go to infinity for r.
并且再次经过,这和，第二块等于0的区域相关联,这也在,我们的概率密度图里反映出来了，然后它又成了正的,并且当r趋于无穷时它趋于。
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We'll introduce in the next course angular nodes, but today we're just going to be talking about radial nodes, psi and a radial node is a value for r at which psi, and therefore, 0 also the probability psi squared is going to be equal to zero.
将会介绍角节点,但我们今天讲的是，径向节点，径向节点就是指，对于某个r的值,当然，也包括psi的平方，等于,当我们说到s轨道时。
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But instead in this chemistry course, I will just tell you the solutions to differential equations. And what we can do is we can start with some initial value of r, and here I write r being ten angstroms. That's a good approximation when we're talking about atoms because that's about the size of and atom.
但在这个课里，我会直接，告诉你们微分方程的解,我们可以给距离r一个初始值,我这里把r取10埃,当我们讨论原子时,这是一个很好的近似,因为原子的尺寸。
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