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。

麻省理工公开课 - 化学原理课程节选

So, if I kind of circle where the probability gets somewhat substantial here, you can see we're much closer to the nucleus at the s orbital than we are for the p, then when we are for the d.

我把概率,很大的地方圈出来，你们可以看到在ｓ轨道上,比ｐ轨道更接近原子核，最远是ｄ轨道。

麻省理工公开课 - 化学原理课程节选

And yet, we know that the shape of the s orbital is spherical.

并且，我们知道S轨道是球状的。

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We talked about the wave function for a 2 s orbital, and also for a 3 s orbital.

我们讲过２ｓ轨道的波函数，也讲过３ｓ轨道。

麻省理工公开课 - 化学原理课程节选

And for a 2 s orbital, you get a graph that's going to look something like this.

对于２ｓ轨道，你们可以得到一个大致是这样的图。

麻省理工公开课 - 化学原理课程节选

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。

麻省理工公开课 - 化学原理课程节选

So, we can see in our 1 s orbital, how many nodes do we have?

有多个节点呢？,没有节点，嗯？

麻省理工公开课 - 化学原理课程节选

So we can also look at this in terms of the 3 s orbital.

我们可以同样的来看下３ｓ轨道。

麻省理工公开课 - 化学原理课程节选

And how many nodes do you see in the 3 s orbital?

那３ｓ轨道有多少个节点呢？

麻省理工公开课 - 化学原理课程节选

So, using the terminology of chemists, which is a good thing to do, because in this course we are all chemists, we want to make sure that we're not using just the physical description of the numbers, but that we can correlate it to 1 0 0 what we understand as orbitals, and instead of 1, 0, 0, 1s we call this the 1 s orbital.

我们最好学会，利用这些化学术语，因为我们这课,就是关于化学的，我们,不仅要知道，这些数字,的物理描述，还要能把它,和我们知道的轨道联系起来，我们叫它。

麻省理工公开课 - 化学原理课程节选

H2 So the simplest case we can think of is with h 2 where we have two unpaired electrons, each in a 1 s orbital of a separate h atom.

最容易想到的例子是2,我们有两个未配对电子，每个都在一个分开的1s轨道上。

麻省理工公开课 - 化学原理课程节选

So, I think we're a little bit out of time today, but we'll start next class with thinking about drawing radial probability distributions of more than just the 1 s orbital.

快没时间了,但我们，在下节课会讲,1s轨道以外的,径向概率分布。

麻省理工公开课 - 化学原理课程节选

And it turns out that if we're talking about a 2 s orbital in an ion, that means it doesn't have as many electrons in it, so what we're going to see is less shielding.

结果是当我们讨论,一个离子中的，2，s，轨道的时候，这意味着里面没有多的电子，那么电子的屏蔽效应会更小。

麻省理工公开课 - 化学原理课程节选

So in other words a very low energy is what we're going to have when we talk about the orbitals -- the energy of the 2 s orbital is going to be less than the energy of the 2 p orbital.

换句话说一个非常低的能量,是我们将会得到的当我们谈论轨道时,2s轨道的,能量比2p轨道,的能量低。

麻省理工公开课 - 化学原理课程节选

For the 2 s orbital, at 2 a nought, a0 so it's just 2 times that constant a nought, which is the Bohr radius.

也就是，乘以常数,玻尔半径，对于3s轨道。

麻省理工公开课 - 化学原理课程节选

s Yeah. And specfically it's the 1 s, so not just the s, but the 1 s orbital.

嗯，它是，不仅是s，是1s轨道。

麻省理工公开课 - 化学原理课程节选

For example, for the 2 s, again what you see is that the multi-electron atom, its 2 s orbital is lower in energy than it is for the hydrogen.

举例来说对于2s轨道，在多电子原子，中可以看到,它的2s轨道的能量低于氢原子的。

麻省理工公开课 - 化学原理课程节选

So that's true for a hydrogen atom, it doesn't matter if you're in a p or an s orbital, their energies are the same.

这对于氢原子来说是这样的，不论是p或，者s轨道，能量是一样的。

麻省理工公开课 - 化学原理课程节选

So, the example that we took on Monday and that we ended with when we ended class, was looking at the 1 s orbital for hydrogen atom, and what we could do is we could graph the radial probability as a function of radius here.

周一我们,最后讲到了，粒子是氢原子１ｓ轨道，我们可以画出,这幅径向概率分布曲线。

麻省理工公开课 - 化学原理课程节选

So what we can say here is that the 2 p is less than or smaller than the 2 s orbital.

所以我们可以说,2p轨道比2s轨道要小。

麻省理工公开课 - 化学原理课程节选

So if we compare l increasing here, so a 3 s to a 3 p to a 3 d, what we find is that it's only in the s orbital that we have a significant probability of actually getting very close to the nucleus.

我们比较当ｌ变大的时候，从３ｓ到３ｐ到３ｄ,我们可以发现只有ｓ轨道,有很大的概率,非常接近原子核。

麻省理工公开课 - 化学原理课程节选

So for a 2 s orbital, how many total nodes will we have?

对于２ｓ轨道，有多少个节点？

麻省理工公开课 - 化学原理课程节选

Let's consider again an s orbital for argon, so let's say we're looking at the 1 s orbital for argon.

我们再考虑一次氩的s轨道，所以我们说我们在看氩的1s轨道。

麻省理工公开课 - 化学原理课程节选

If you compare the s orbital with the bottom lobe, these have a different sign so they're going to destructively interfere.

如果你们比较s轨道和下面这叶，它们正负号相反,所以它们相消干涉。

麻省理工公开课 - 化学原理课程节选

And then this means we'll have a total of sigma1s two electrons in our hydrogen molecule, so we can fill both of those into the sigma 1 s orbital, the bonding orbital. We don't have to put anything into the anti-bonding orbital, so that's great.

我们可以把这两个,都填入，轨道里去，成键轨道,我们不需要把什么放到反键轨道里去，这很好。

麻省理工公开课 - 化学原理课程节选

So we have two nodes in the 3 s orbital.

我们可以确定。

麻省理工公开课 - 化学原理课程节选

s -- we don't have to hybridize it, it already has only one unpaired electron in a 1 s orbital.

s-我们不用杂化它，它已经有而且仅有一个未配对电子在s轨道里。

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。

麻省理工公开课 - 化学原理课程节选

And then we're going to name the atomic orbitals that make it up, and it's being made up of a carbon 2 s p 3 orbital, and a hydrogen 1 s orbital.

然后我们要命名,组成它的原子轨道，它是由碳2sp3轨道，和氢原子1s轨道组成。

麻省理工公开课 - 化学原理课程节选

So, what we call this is the third ionization energy, or the negative of the binding energy, again of the 2 s orbital, but now it's in boron plus 2 to we're starting with.

那么我们称它为第三电离能，或者负的束缚能，还是，2，s，轨道的，但现在我们是从正二价硼离子开始的。

麻省理工公开课 - 化学原理课程节选