So, let's go ahead and think about drawing what that would look like in terms of the radial probability distribution.

让我们来想一想如果把它的,径向概率分布画出来是怎么样的。

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This is the radial probability distribution formula for an s orbital, which is, of course, dealing with something that's spherically symmetrical.

这个ｓ轨道的,径向概率分布公式，它对于球对称,的情形成立。

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Central tendency is a measure of the center of a probability distribution of the-- Central tendency is a measure-- Variance is a measure of how much things change from one observation to another.

集中趋势用以描述,一组概率分布的中心,集中趋势...,而方差衡量的是,各个观察值之间的变化

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But still, when we're talking about the radial probability distribution, what we actually want to think about is what's the probability of finding the electron in that shell?

但当我们讲到径向概率分布时,我们想做的是考虑，在某一个壳层里,找到电子的概率,就把它想成是蛋壳？

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It's somewhat different when we're talking about the p or the d orbitals, and we won't go into the equation there, but this will give you an idea of what we're really talking about with this radial probability distribution.

当我们讨论ｐ轨道或者,ｄ轨道的时候会有些不同，我们那时不会给出方程，但它会给你们一个,关于径向概率,分布的概念。

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So if we superimpose our radial probability distribution onto the Bohr radius, we see it's much more complicated than just having a discreet radius.

为波尔半径,这其实比分立的轨道,要复杂很多，我们可以有任何的半径,但有些半径的概率。

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Or we could just look at the radial probability distribution itself and see how many nodes there are.

或者我们可以直接,看径向概率分布图,本身看看里面有几个节点。

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But there's also a way to get rid of the volume part and actually talk about the probability of finding an electron at some certain area within the atom, and this is what we do using radial probability distribution graphs.

除去体积部分,来讨论,在某些区域内,发现一个原子的概率,我们可以，用，径向概率分布图,它是。

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We will always have r equals zero in these radial probability distribution graphs, and we can think about why that is.

在这些径向概率分布图里,总有ｒ等于０处，我们可以考虑为什么会这样。

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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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So, let's actually compare the radial probability distribution of p orbitals to what we've already looked at, which are s orbitals, and we'll find that we can get some information out of comparing these graphs.

让我们来比较一下ｐ轨道,和我们看过的,ｓ轨道的径向概率分布，我们发现我们可以通过,比较这些图得到一些信息。

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So here, what I'd like you to do is identify the correct radial probability distribution plot for a 5 s orbital, and also make sure that it matches up with the right number of radial nodes that you would expect.

这里，你们要辨认,哪个是５ｓ轨道的正确概率分布，并且确保它和你们,预期的节点数相符合。

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If you wrote only one policy, what's the probability distribution of x/n?

如果你只签了一份保单,那么x/n的概率分布是怎样的?

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And in doing that, we'll also talk about the shapes of h atom wave functions, specifically the shapes of orbitals, and then radial probability distribution, which will make sense when we get to it.

为了这样做，我们要讲一讲，氢原子，波函数的形状，特别是轨道的形状，然后要讲到径向概率分布，当我们讲到它时，你们更能理解。

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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。

麻省理工公开课 - 化学原理课程节选

so when we think about what it is that this radial probability distribution is telling us, it's telling us that it is most likely that an electron in a 2 s orbital of hydrogen is six times further away from the nucleus than it is in a 1 s orbital.

我们来讨论一下这个径向概率分布,告诉了我们什么，它告诉我们,对于氢原子２ｓ轨道的电子,最可能位置是１ｓ轨道的６倍。

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So, there are 2 different things that we can compare when we're comparing graphs of radial probability distribution, and the first thing we can do is think about well, how does the radius change, or the most probable radius change when we're increasing n, when we're increasing the principle quantum number here?

当比较这些径向概率分布图,的时候，我们可以比较两个东西，第一个就是考虑当我们增加ｎ,当我们增加主量子数的时候，半径怎么变，最可能半径怎么变化？

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What is the probability distribution for x/n in that case?

在这样的情况下,x/n的概率分布是怎样的

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F is the continuous probability distribution for x.

是x的连续型随机变量的概率分布

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If you follow through from the independent theory, there's one of the basic relations in probability theory-- it's called the binomial distribution.

如果继续往下看,在概率论里有一个基本的概念,叫做二项分布

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It uses the binomial distribution to calculate the probability of getting any specific number of accidents.

保险公司就可以用二项分布公式,来计算特定数目事故发生的概率

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