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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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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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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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Ah, but density is mass over volume.
但密度是质量除以体积
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Okay, the higher caloric density.
没错,高热量密度
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You've probably seen agar plates, if you smear a solution that's contaminated with bacteria on it, then that bacteria will grow on this agar rich medium and you'll get many, many copies of the bacteria that you've smeared at low density onto the plate.
你们大概见过琼脂培养基,如果将有细菌的溶液涂抹在培养基上,细菌就会在富含琼脂的培养基上生长,你会得到许多许多细菌,即使你只涂抹了低浓度溶液
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So for example, that might have a formal charge of negative 1, because to some extent it has gained that much electron density that it now has a formal charge that's negative.
比如，可能它的形式电荷为负一，因为在一定程度上它得到了这么多的共用电子密度,那么它现在就有了负的形式电荷。
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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 he predicts the density of the oxide of the yet undiscovered element.
他预测这个还未被发现的元素的,氧化物的密度。
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So, one way we could look at it is by looking at this density dot diagram, where the density of the dots correlates to the probability density.
其中一个理解它的方法,就是通过看这个密度点图，这里点的密度,和概率密度想关联的。
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So you can think about how these 2 things combined are going to be electronegativity, which is a measure of how much an atom wants to pull electron density away from another atom.
因此你可以想象出,这两样性质合起来就是电负性，也就是一个度量，关于一个原子,有多希望把另一个原子的电子密度拉过来的。
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So again if we look at this in terms of its physical interpretation or probability density, what we need to do is square the wave function.
如果我们从物理意义或者,概率密度的角度来看这个问题，我们需要把波函数平方。
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But a real key in looking at these plots is where we, in fact, did go through zero and have this zero probability density.
是我们经历这些零值,而且有这些零概率密度,我们把它叫做节点。
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So it's just a measure of how much does one given atom want to pull away electron density from, let's say, an adjacent atom.
因此，它就是度量一个给定原子有多么,想把电子密度拉过来，可以说，从相邻的一个原子那里。
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So if I try to rotate my 2 atoms, you see that I have to break that pi bond, because they need to be lined up so that the electron density can overlap.
如果我要试着转动两个原子，你会看到我必须要打破一个π键，因为他们需要连接起来,让那些电子能够重叠。
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This is not a node because a node is where we actually have no probability density.
因为节点处是,没有概率密度的,所以。
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So again, we can think about the probability density in terms of squaring the wave function.
同样的，我们可以把,波函数平方考虑概率密度。
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So, what we're going to define is just let's just capture 90% of that electron density.
所以，我们所定义的,只包括百分之九十的电子密度。
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Probability density of finding an electron within that molecule in some given volume.
在分子内某空间找到,一个电子的概率密度。
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So what is actually going to matter is how closely that electron can penetrate to the nucleus, and what I mean by penetrate to the nucleus is is there probability density a decent amount that's very close to the nucleus.
所以实际上有关系的是,电子可以穿越至原子核有多近,我所指的穿越至原子核是,这里有一定数量的概率密度,可以距离原子核非常近。
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Again, we have continuous electron density from one nucleus to the other.
再说一遍，原子核间有不间断的电子云,相接没有节点，没有空缺。
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So, the quantum mechanical interpretation is that we can, in fact, have probability density here and probability density there, without having any probability of having the electron in the space between.
量子力学给出的解释是，实际上，我们可以在这有概率密度，在这里有概率密度,但在两个之间没有。
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This should make sense because if something has a low ionization energy, that means it's not very electronegative, which means it's going to be a lot happier giving up electron density, which is essentially what you're doing -- when you're forming covalent bonds is you're sharing some of your electron density.
这应该是合理的,因为如果某物的电离能很低，这也就意味着它的电负性也不高，那么它就会更愿意,放弃一定的电子密度，而本质上这正是你在,形成共价键时所需要做的,分享你的一些电子密度。
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