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I have a final question for you: do you feel that Princeton university is on the right trajectory in answering the question of just university?
我再问你们最后一个问题，你们认为,普林斯顿大学是否在正确的轨道上发展么？,我指的是在公正的实践这一方面？
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What is the filling sequence of electrons in orbitals?
什么是电子在轨道上的排布顺序呢？
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So what that means is that we're limited in any atom to having two electrons per orbital, right, because for any orbital we can either have a spin up electron, a spin down electron, or both.
这意味着在一个原子内,每个轨道上可以有两个电子，对吧，因为对任何轨道,我们可以有自旋向上或者自选向下或者两者都有。
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Suppose you're the driver of a trolley car, and your trolley car is hurtling down the track at 60 miles an hour.
假设你是一名电车司机，你的电车以60英里/小时的速度,在轨道上飞驰。
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If you escape the pull of gravity, your spaceship will be off, won't be orbiting the Earth.
如果你完全脱离重力,太空船早就飞得没影了,而不是在轨道上运行
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So, if you're looking back, say, from the end of the nineteenth century, it's not easy to see, but you can see these-- don't ever think that history runs on railroad tracks, and all you need is the timetable to show when modernization shows up.
所以,当你回顾历史,从十九世纪的末尾开始,虽然不太容易,但还是可以看出...,别以为历史是在固定轨道上行进的,别以为你只用拿时刻表,就知道新时代什么时候来临
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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。
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So even though we see a nodal plane down the center, I just want to really point out that it's only when we have a nodal plane in the internuclear or the bond axis that we're calling that a pi orbital.
虽然在中间有个节面，我想要指出的是,只有节面在核间轴,或者键轴上时,我们才叫它π轨道。
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Electrons will occupy orbitals in order of ascending energy, occupying the lowest energy first and up.
电子是按其能量递增顺序,排布在轨道上的，首先占满第一级，即最低能级。
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So we're going to limit in our discussion in 511-1 for molecular orbital theory to diatomic molecules.
我们在这个课堂上对分子轨道1,理论的讨论仅限于双原子分子。
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He would fall over the bridge onto the track right in the way of the trolley car.
他就会摔下桥,正好摔在电车轨道上挡住电车。
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And orbiting around this is a lone electron out at some distance r.
有一个单电子,在环原子核的轨道上运行。
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And a sigma bond forms any time you have two orbitals coming together and interacting on that internuclear axis.
当你把两个轨道合在一起,并在核间轴上有相互作用时,就形成了sigma键。
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Any time two orbitals come straight on together in that internuclear axis, you're going to have a sigma bond.
任何时候两个轨道,在核间轴上直接到一起，你就能得到sigma键。
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You have two electrons in antibonding to kind of offset the bonding.
你有两个电子,在远离成键轨道的反键轨道上。
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You're standing on a bridge overlooking a trolley car track.
你站在一座桥上，俯瞰着电车轨道。
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There's no more 2 p orbitals to put it into, so we're going to actually have to double up.
现在并没有多余的2，p，轨道来放它，我们只能在其中一个，2，p，轨道上放上两个。
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I am going to say if that electron is to stay in its orbit, that is to say it doesn't flee the atom, it doesn't collapse under the nucleus then the sum of the forces on the electron must be zero No net force. And so that will be the sum of a dynamic force plus an electrostatic.
如果电子会保持在它的轨道上运行,既不脱离原子的话，它就不会由于原子核对它的吸引力而被瓦解掉,电子所受的合力一定为零,由于没有合力,所以电子所受力为动态力和静电力的总和。
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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。
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So you can see here in this slide we have the atomic orbitals for the two hydrogen atoms, each of them have one electron in them, hydrogen has one electron in a 1 s orbital.
从这个幻灯片你们可以看到我们,有这两个氢原子的原子轨道，每个上面有个电子，氢原子上面有一个电子在1s轨道上。
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So this is a little bit trickier to look at and see what it means, but essentially we have two hybrid orbitals, which are shown in blue here, and then we have one p orbital that's left alone that's going up and down on the page.
看这个图肯能会觉得比较诡异，但本质上，骂我们有两个杂化轨道，这里用蓝色表示，还有剩下一个p轨道,在图中上下方向上。
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So now we're putting 2 electrons into the same p orbital, that's not a problem, we can do it, it's not a huge energy cost to do that.
现在我们在同一个，p，轨道上放了两个电子，这没问题，我们可以这样做，这样不会亏损太多能量。
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The reason that it's a sigma bond is sp3 because the s p 3 hybrid orbital is directly interacting with the 1 s orbital of the hydrogen atom, and that's going to happen on the internuclear axis, they're just coming together.
它是sigma键的原因,是因为,杂化轨道直接和氢原子1s轨道相互作用，它们作用发生在核间轴上，它们会到一起。
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We can actually specify where those nodes are, 2a0 which is written on your notes.
这些节点在哪，这在你们的讲义上写出来了，对于2s轨道，在。
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So think about what that means, we're, of course, not talking about this in classical terms, so what it means if we have an electron in the 2 p orbital, it's more likely, the probability is that will be closer to the nucleus than it would be if it were in the 2 s orbital.
想想这意味着什么，我们不是从经典的角度考虑，这意味着如果我们有个电子在2p轨道上，它更有可能比在2s轨道上,更加靠近原子核。
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I have two lobes in a p-orbital.
在一个p轨道上我们有两个叶。
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We're having two orbitals coming together on the bond axis.
我们在这个轴上有两个轨道相互靠近。
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So, I want to contrast that with another concept that seemed to be opposing ideas, and that is thinking about not how far away the most probable radius is, but thinking about how close an electron can get to the nucleus if it's actually in that orbital.
我要将它和另外一个,看起来相反的概念相比较，我们不是考虑,最可能半径离原子核有多远，而是考虑如果电子在那个轨道上,能多接近原子核。
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But actually there is a little bit of an energy cost into doubling up into a single orbital, because, of course, it takes energy when you create more electron repulsion, that's not something we want to do, but we have to do it here, and it turns out that that effect predominates over, again, the energy that we gain by increasing the atomic number by one.
但实际上，在一个轨道上放两个电子,确实会亏损一点能量，因为，当你加入更多电子，引起更大的排斥能,这显然会消耗能量，这不是我们想要做的，但是在这种情况下我们不得不做，结果这一影响，超过了增加一个,原子序数所得到的能量。
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So basically, that means one electron in an s orbital in their outer-most most shell.
因此基本上,这意味着那个在，s，轨道上价电子是最外层的。
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