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Let's look at the energetics of one of those electrons crashing into a hydrogen atom inside the gas tube.
我们一起来考察一下,其中的一个电子的能量,在阴极射线管中,撞击到氢原子上。
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So, what we get for the disassociation energy for a hydrogen atom is 424 kilojoules per mole.
因此，我们就得到了氢原子,离解能的大小为，424，千焦每摩尔。
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Also, when we're looking at the Schrodinger equation, it allows us to explain a stable hydrogen atom, which is something that classical mechanics did not allow us to do.
当我们看一个薛定谔方程的时候，它给出一个稳定的氢原子,这是在经典力学中做不到的。
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Here we're talking about a hydrogen atom and that's what we'll focus on today. And it's incredibly precise and we're able to make the predictions and match them with experiment.
是一个氢原子，我们今天都主要讨论它,它非常准确，我们可以做出,预测与实验比较，此外。
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So if we're talking about the fourth excited state, and we talk instead about principle quantum numbers, what principle quantum number corresponds to the fourth excited state of a hydrogen atom.
如果我们说的是,第四激发态，我们用,主量子数来描述，哪个主量子数对应了,氢原子的第四激发态？
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And I just want to point out here in terms of things that you're responsible for, you should know that the most probable radius for a 1 s hydrogen atom is equal a nought.
在这里,我想要指出的是，你们要知道氢原子１ｓ轨道,最可能距离等于ａ０
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So, for example, in a hydrogen atom, if you take the binding energy, the negative of that is going to be how much energy you have to put in to ionize the hydrogen atom.
例如在氢原子里面,如果你取一个结合能,它的负数就是。
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It turns out, and we're going to get the idea of shielding, so it's not going to actually +18 feel that full plus 18, but it'll feel a whole lot more than it will just feel in terms of a hydrogen atom where we only have a nuclear charge of one.
结果是我们会有,屏蔽的想法,所以它不会是完整的，但是它会比原子核电荷量,吸引力要大很多,只有1的氢原子的。
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So, what we know is happening is that were having transitions from some excited states to a more relaxed lower, more stable state in the hydrogen atom.
我们知道，这里所发生的是,氢原子从激发态到更低更稳定的态的跃迁，而我们用眼睛可以探测到的。
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So let's compare what some of the similarities and differences are between hydrogen atom orbitals, which we spent a lot of time studying, and now these one electron orbital approximations for these multi-electron atoms.
很长时间的氢原子轨道和,现在多电子原子中,的单个电子轨道近似，我们可以对比，它们之间,的相似性和不同。
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And there again is another difference between multi-electron atom and the hydrogen atoms.
在多电子原子和氢原子,之间还有一个区别,当我们谈论多电子原子轨道时。
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So here I've written for the hydrogen atom that deceptively simple form of the Schrodinger equation, where we don't actually write out the Hamiltonian operator, but you remember that's a series of second derivatives, so we have a differential equation that were actually dealing with.
这里我写出了,氢原子薛定谔方程的,最简单形式，这里我们实际上,没有写出哈密顿算符,但是请记住那你有，一系列的二次导数,所有我们实际上会处理一个微分方程。
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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。
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and he knew this the same way that we saw it in the last class, which is when we viewed the difference spectra coming out from the hydrogen, and we also did it for neon, but we saw in the hydrogen atom that it was very discreet energy levels that we could observe.
那就是,当我们看氢原子发出的光谱时，我们也看了氖气,但我们看到,氢原子能级是分立的，这些，在当时,已经被观察到了,他也都知道。
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So, in talking about covalent bonds, we should be able to still apply a more general definition of a chemical bond, which should tell us that the h 2 molecule is going to be lower in energy than if we looked at 2 separate hydrogen atom molecules.
那么，既然提到了共价键，我们应该还可以,给化学键下一个更普遍的定义,那就是告诉我们氢分子能量应该更低,与两个分开的氢的单原子分子相比。
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And we also, when we solved or we looked at the solution to that Schrodinger equation, what we saw was that we actually needed three different quantum numbers to fully describe the wave function of a hydrogen atom or to fully describe an orbital.
此外，当我们解波函数,或者考虑薛定谔方程的结果时，我们看到的确３个不同的量子数,完全刻画了氢原子,的波函数或者说轨道。
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So when we talk about the size of multi-electron orbitals, they're actually going to be smaller because they're being pulled in closer to the nucleus because of that stronger attraction because of the higher charge of the nucleus in a multi-electron atom compared to a hydrogen atom.
所以当我们讨论,多电子轨道的尺寸，它们实际上会变得更小,因为多电子原子的原子核,相比于氢原子,有更高的电荷量所以,有更强的吸引力,所以可以拉的更近。
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So today, we're going to start talking about the hydrogen atom.
今天我们将谈到氢原子。
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So, let's look at what this actually is for what we're showing here is the 1 s hydrogen atom.
让我们来看看,我们这里给出的这个氢原子1s轨道,到底是什么。
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So there's one electron in each hydrogen atom.
所以每个氢原子中有两个电子。
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And hydrogen atom is what we're learning about, so that's the most relevant here. But just to show you that each atom does have its own set of spectral lines, just for fun we'll look at neon also so you can have a comparison point.
为了给你们展示下每个原子，都有自己的一套谱线,仅仅是为了好玩，我们看下氖,你们可以比较一下。
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And when we talked about that, what we found was that we could actually validate our predicted binding energies by looking at the emission spectra of the hydrogen atom, which is what we did as the demo, or we could think about the absorption spectra as well.
当我们讨论它时，我们发现,我们可以通过,观察氢原子,发射光谱，来预测，结合能，就像我们在演示实验里做的那样，或者我们也可以观察吸收谱。
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So let's say, for example, in a hydrogen atom.
比如说，在氢原子里。
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So another way to say that is, in a sense, if we're thinking about the excited state of a hydrogen atom, the first excited state, or the n equals 2 state, what we're saying is that it's actually bigger than the ground state, or the 1 s state of a hydrogen atom.
换句话说，如果我们激发一个氢原子，第一激发态或者说ｎ等于２的态，我们说它比氢原子基态,或者说１ｓ态要大。
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And we can look at precisely why that is by looking at the equations for the energy levels for a hydrogen atom versus the multi-electron atom. So, for a hydrogen atom, and actually for any one electron atom at all, this is our energy or our binding energy.
而且我们可以精确地看看,为什么是这样的,通过看对于氢原子和,多电子原子能级的方程所以对于氢原子，事实上对于任何一个电子，这是我们的能量或者我们的结合能。
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We've got a lot of constants in this solution to the hydrogen atom, and we know what most of these mean. But remember that this whole term in green here is what is going to be equal to that binding energy between the nucleus of a hydrogen atom and the electron.
在这个解中有很多常数,其中大部分我们,都知道它们代表的意思,但记住是这整个绿色的部分,等于核子和电子的结合能。
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So, let's take a look here at an example of an energy diagram for the hydrogen atom, and we can also look at a energy diagram for a multi-electron atom, and this is just a generic one here, so I haven't actually listed energy numbers, but I want you to see the trend.
所以让我们来看看,一个例子氢原子的能量图，我们也可看看一个,多电子原子的能量图，这是一个普通的图谱，我没有列出能量的数字，但是我想让你们看这个趋势。
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I have yet to show you the solution to a wave function for the hydrogen atom, so let me do that here, and then we'll build back up to probability densities, and it turns out that if we're talking about any wave function, we can actually break it up into two components, which are called the radial wave function and angular wave function.
我还没有给你们看过,氢原子波函数的解，让我现在给你们看一下，然后再来说,概率密度，实际上,对于任何一个波函数来说，我们可以把它,分解为两部分，分别叫做径向波函数,和角向波函数。
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So for example, if you look at the 1 s orbital here, you can see that actually it is lower in the case of the multi-electron atom than it is for the hydrogen atom.
所以举例来说，如果你看到这里的1s轨道,你可以看到实际上,多电子原子情况的。
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