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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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。

麻省理工公开课 - 化学原理课程节选

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。

麻省理工公开课 - 化学原理课程节选

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。

麻省理工公开课 - 化学原理课程节选

So, at this place where it hits zero, 0 that means that the square of the wave function is also going to be zero, right.

它达到0的地方，这意味着波函数的，平方也是,如果我们看概率密度图。

麻省理工公开课 - 化学原理课程节选

And when we're looking at the probability density graphs, it doesn't make a difference, it's okay, It has no meaning for our actual plot there, because we're squaring it, so it doesn't matter whether it's negative or positive, all that matters is the magnitude.

它的概率密度图的时候,两者没什么区别，这是可以的，它对我们画这个图，没有什么意义,因为我们是取平方，所以它的正负，无所谓，只和幅值有关，但当我们说到。

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This is the probability density map, so we're talking about the square here.

这是它的概率密度图，我们看的是平方。

麻省理工公开课 - 化学原理课程节选

Think of it as a probability density plot.

把它看成是一个概率密度图。

麻省理工公开课 - 化学原理课程节选

So, again we can use these probability density plots, which are just a plot of psi squared, where the density of the dots is proportional to the density, the probability density, at that point.

同样的我们可以利用这些概率密度图，这是psi的平方的图，这里面点的密度，正比于概率密度。

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。

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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。

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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？

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