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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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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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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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You can see down here its affect on cholesterol levels: that the bad fats raise the LDL levels, the low-density lipoproteins levels, that's not good for you.
在下面你可以看到它对胆固醇含量的影响,坏脂肪会提高LDL含量,低密度脂蛋白含量,这是对身体不好的
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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 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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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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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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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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The first one will be above and below the bond axis is where we'll see the electron density, and the second will be perpendicular to that, so it will be a density in front of and behind the bond axis.
第一个是在键轴之上和之下,我们可以看到电子密度，另外一个垂直于它，所以在键轴之前和之后有电子密度。
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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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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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We'll start with talking about the shape, just like we did with the s orbitals, and then move on to those radial probability distributions and compare the radial probability at different radius for p orbital versus an s orbital.
想我们对待ｓ轨道那样，我们先讨论ｐ轨道的形状，然后是径向概率密度分布,并且把ｓ轨道和ｐ轨道在,不同半径处的径向概率做一个比较。
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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, 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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So, when we're talking about the idea of electronegativity, essentially what we're talking about is the ability for an atom to attract electron density from another atom.
那么，当我们在讨论电负性这一概念的时候，本质上我们讨论的是一个原子的吸引能力,用来吸引另一个原子的电子密度的。
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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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6 It's got a density of about 1.76 at room temperature.
在室温下密度是1。
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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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So, for example, we have this average level, and then it can go high where we have the peak, or it can go very low. We can also discuss sound waves, so again it's just the periodic variation of some property -- in this case we're talking about density, so we have high density areas and low density areas.
例如这是平均位置，在峰的位置水位高，在谷水位低，我们也可以,讨论声波它也是某种,量的周期变化，在这里我们,讨论的是密度,我们有高密度区和低密度区。
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a perfectly spherical shell dr at some distance, thickness, d r, dr we talk about it as 4 pi r squared d r, so we just multiply that by the probability density.
在某个地方的完美球型壳层,厚度，我们把它叫做4πr平方，我们仅仅是把它,乘以概率密度。
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So we can think of a third case where we have the 3 s orbital, and in the 3 s orbital 0 we see something similar, we start high, we go through zero, where there will now be zero probability density, as we can see in the density plot graph.
第三个例子那就是,3s轨道,在3s轨道里，我们看到类似的现象,开始非常高，然后穿过，这里，概率密度是0，就像你们在概率密度图里看到一样，然后我们到负的。
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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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And if we go ahead and square that, then what we get is a probability density, and specifically it's the probability of finding an electron in a certain small defined volume away from the nucleus.
我们得到的是，一个概率密度，它是，在核子周围，某个很小的,特定区域,找到电子的概率,所以它是概率密度。
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So, basically what we're saying is if we take any shell that's at some distance away from the nucleus, we can think about what the probability is of finding an electron at that radius, and that's the definition we gave to the radial probability distribution.
本质上我们说的就是,如果我们在距离原子核,某处取一个壳层，我们可以考虑在这个半径处,发现电子的概率，这就是我们给出的,径向概率密度的定义。
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So there's electron density above the bond and below the bond.
所以在键轴上面和下面都有电荷密度。
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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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