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。

麻省理工公开课 - 化学原理课程节选

The answer is, in fact, there is zero, absolutely zero probability of finding a electron here.

实际上它在这里是为零的，在这里找到电子的概率严格等于零。

麻省理工公开课 - 化学原理课程节选

If the probability is zero that means the event can't happen.

如果概率等于0就意味着事件不会发生

耶鲁公开课 - 金融市场课程节选

So, if we say that in this entire plane we have zero probability of finding a p electron anywhere in the plane, the plane goes directly through the nucleus in every case but a p orbital, so what we can also say is that there is zero probability of finding a p electron at the nucleus.

而只要是ｐ轨道,这个平面都直接，穿过原子核，那么我们,可以说在原子核上,找到一个ｐ电子的概率为零。

麻省理工公开课 - 化学原理课程节选

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．

麻省理工公开课 - 化学原理课程节选

So, that can be a little bit confusing for us to think about, and when it's a very good question you might, in fact, say well, maybe there's not zero probability here, maybe it's just this teeny, teeny, tiny number, and in fact, sometimes an electron can get through, it's just very low probability so that's why we never really see it.

这想起来有点令人困惑，你们可能会说也许，这里的概率并不是严格的为零，而是非常非常小，所以有时电子就可以穿过去，这是个,很好的想法。

麻省理工公开课 - 化学原理课程节选

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。

麻省理工公开课 - 化学原理课程节选

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。

麻省理工公开课 - 化学原理课程节选

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。

麻省理工公开课 - 化学原理课程节选

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。

麻省理工公开课 - 化学原理课程节选

If the probability is 1 in 1,000 that a house burns down and there are 1,000 houses, then the probability that they all burn down is 1/1000 to the 1000th power, which is virtually zero.

如果一栋房子着火的概率是千分之一,然后假设有1000栋房子,那么这一千栋房子全都着火被烧掉的概率,就等于千分之一的一千次方,基本上就是0了

耶鲁公开课 - 金融市场课程节选

The reason in our radial probability distributions we start -- the reason, if you look at the zero point on the radius that we start at zero is because we're multiplying the probability density by some volume, and when we're not anywhere 0 from the nucleus, that volume is defined as zero.

在径向概率密度里，我们开始,如果你们看半径的零点，我们从零点开始,因为我们用概率密,度乘以体积,而当我们，在离核子很近的地方,体积是，所以我们会在这里。

麻省理工公开课 - 化学原理课程节选

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。

麻省理工公开课 - 化学原理课程节选

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。

麻省理工公开课 - 化学原理课程节选

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。

麻省理工公开课 - 化学原理课程节选

We call that a node, r and a node, more specifically, is any value of either r, the radius, or the two angles for 0 which the wave function, and that also means the wave function 0 squared or the probability density, is going to be equal to zero.

节点就是指对，于任何半径，或者，两个角度,波函数等于，这也意味着波函数的平方或者概率密度,等于，我们可以看到在1s轨道里。

麻省理工公开课 - 化学原理课程节选

It looks like we hit zero, but we actually don't remember that we never go all the way to zero, so there's these little points if we were to look really carefully at an accurate probability density plot, And then, for example, how many nodes do we have in the 3 s orbital?

但其实没有，记住，我们永远不会到零,如果我们，在概率密度图上,非常细致的看这些点的话,它永远不会到零，在3s轨道里，有多少个点呢？，2个，正确？

麻省理工公开课 - 化学原理课程节选