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It's one of the only compounds, there's only I think three, where the density actually goes down when it freezes.
它是我见过的，唯一一个，在降温时密度下降的化合物。
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Our friend Schr?dinger told us that if you solve for the wave function, this is what the probability densities look like.
我们的朋友薛定谔告诉我们,如果你用波函数来解决，你就会知道这些概率密度看上去的样子。
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We can graph out what this is where we're graphing the radial probability density as a function of the radius.
我们可以，画出它来,这是径向概率密度,作为半径的一个函数图。
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You make the volume infinitely large, the density of the gas infinitely small.
密度无限小，气体分子之间的相互作用。
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What the Dutch did--the Netherlands is an extraordinarily small country, and it's the most populated country in Europe, then, per square kilometre, and is now--once.
那些荷兰人...荷兰是一个,非常非常小的国家,也是当时欧洲人口密度最高的国家,如果以每平方公里人口计算,现在也是
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We have instead what's called a probability density when we have continuous random variables.
所以我们用概率密度的概念来描述,连续型随机变量的情况
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How is anyone going to give you a density of anything?
你怎样获得任意物体的密度
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Sometimes we have a very electronegative atom that's going to take more of its equal share of electron density.
有时候我们会有一个电负性很高的原子,它将会获取更多的共用电子密度。
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We can talk about the wave function squared, the probability density, or we can talk about the radial probability distribution.
我们可以讨论它,波函数的平方，概率密度，或者可以考虑它的径向概率分布。
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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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Think of anything else with the density goes down when it freezes, and think about where we would be if that wasn't the case.
想想有没有其他的物质,在降温时密度会变大，再想想如果不是这种情况,我们将会怎么样。
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And then he says the tetrachloride will be volatile, 9 and it will have a density of 1.9.
他说四氯化物具有不稳定性，密度是1。
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And you see that the dot intensity grows as you get closer and closer to the center.
点的密度随着到中心的距离,缩短的变密。
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Great. Yup, it's going to be an electron acceptor, it wants to accept electrons, it wants to accept electron density.
很好，没错，它将是一个电子的受主，它想要接收电子，接收电子密度。
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So, doing those probability density dot graphs, we can get an idea of the shape of those orbitals, we know that they're spherically symmetrical.
概率密度点图上,我们可以对这些轨道的形状，有个大概了解,我们知道它们是球，对称的,我们今天不讲。
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But we can also think when we're talking about wave function squared, what we're really talking about is the probability density, right, the probability in some volume.
波函数平方,的时候，我们说的，是概率密度，对吧,是在某些体积内的概率，但我们有办法。
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So we can see if we look at the probability density plot, we can see there's a place where the probability density of is actually going to be zero.
就能看到,有些地方，找到一个电子的,概率密度,我们可以考虑。
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And when we take the wave function and square it, that's going to be equal to the probability density of finding an electron at some point in your atom.
当我们把波函数平方时，就等于在某处,找到一个电子的概率密度。
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So again, this is an anti-bonding orbital, and what you see is that there is now less electron density between the two nuclei than there was when you had non-bonding.
同样的，这是反键轨道，你们看到当你有反键轨道的时候,两个原子核中间的电子密度更小了。
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The reason that there is increased electron density here is you can see that these two orbitals come together and constructively interfere.
你们可以看到两个轨道,靠在一起相长叠加,这就是为什么中间的电子态密度增加了。
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So, what you see is near the nucleus, the density is the strongest, the dots are closest together.
你看在核子附近，密度非常高，这些点非常密。
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So, instead of having the periodic variation of water, or the periodic variation of air density here we're talking about an electric field.
不像水或者空气密度的,周期变化，我们这里,讨论的是电场。
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At first it might be counter-intuitive because we know the probability density at the nucleus is the greatest.
起初我们觉得这和直观感觉很不相符,因为我们知道在原子核,出的概率密度是最高的。
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And we know that it's electron density between the nuclei that holds two atoms together in a bond.
我们知道是两个原子核之间的,电子密度保持两个原子在一起成键的。
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So, that's probability density, but in terms of thinking about it in terms of actual solutions to the wave function, let's take a little bit of a step back here.
这就是概率密度，但作为,把它当成是，波函数的解，让我们先倒回来一点。
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When we were talking about constructive interference, we had more electron density in between the 2 nuclei.
当我们讨论相长干涉的时候，在两个原子核之间有更多的电子密度。
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And so, the radial probability density at the nucleus is going to be zero, even though we know the probability density at the nucleus is very high, that's actually where is the highest.
所以径向概率密度,在核子处等于零，虽然我们知道在，核子处概率密度很大,实际上在这里是最大的，这是因为。
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All right, so that will now allow you to turn the page, I think, and we can take a look at the probability.
好了，现在你们可以翻过这页了，让我们看一看概率密度。
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So what we should expect to see is one radial node, and that is what we see here 3s in the probability density plot.
个节点,这就是我们，在这概率密度图上所看到的,如果我们考虑。
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Anywhere where that's the case we're going to have no probability density of finding an electron.
这时面内任何地方,找到电子的概率密度都是零。
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