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So, let's say we're talking about the baseball, have a wavelength of the baseball that's on the order of the baseball.
克服质量的效应，比如说以棒球为例,要棒球的波长有它尺寸数量级的波长。
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If I get you down to a cluster of about 30 water molecules, the boiling point is a function of the size of the water droplet.
如果对于一个由30个水分子,组成的簇，沸点是,水珠尺寸的函数。
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So, the size still for an s orbital is larger than for a d orbital, but what we say is that an s electron can actually penetrate closer to the nucleus.
轨道的尺寸比,ｐ轨道还是要大，但我们说的是ｓ轨道可以,穿透到更接近原子核的地方。
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And the answer has to do with ratios and string sizes and lengths of pipe and things like that, but generally speaking, pitches that are right next to each other--very close to each other--are dissonant.
答案和比率以及弦乐器的尺寸和管乐器的长度等有关，但是总的说来，音调是相关联的，非常近。
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Well, if I go through that, the wavelength of such a photon is going to be so big that I am back to measuring the dimension of the human hair with the yardstick.
好的，如果我做完了这个，那个一光子的的波长将成为,我将回头测量的,用一个尺度测量出人头发的尺寸。
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The way he described is when you try to get down a quantum dimensions and you are standing there with your camera, just remember the sun is at your back and your shadow is always in the picture.
这种方法被他描述为,当你试着处理一个量子尺寸时,并且你试着拿着你的相机在那，记住太阳在你的背后,而你的影子总是在照片上。
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So, in terms of wavelength, Wakefield has the largest wavelength, but in terms of being significant, we're still not even close.
所以，Wakefield投出的球，有最大的波长，但是从可比性来讲，它实际仍未接近球的尺寸。
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So if we're keeping n the same, we look and what we saw was that size actually decreases as we increase the value of l.
如果我们保持ｎ不变，我们看到随着ｌ值的,增大尺寸变小。
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So this is, first of all, even just on an absolute scale, this is way, way larger than the wavelengths we're talking about for baseball.
首先，即使在一个绝对标度下，棒球的尺寸也,远远地大于它的波长。
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So we say if n increases, the orbital size is also going to increase.
轨道的尺寸，也增大了。
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People to this day are looking for a theory of everything. And there is something very appealing about the notion that the rules that govern the motion of heavenly bodies might be applicable down at atomic dimensions.
现在人们总想寻求一些,可以阐明一切的理论,而这里正好有一些,可以吸引这种想法的东西,即支配天体运动的规则,可能对原子的尺寸也是适用的。
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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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We know that this dimension is roughly one angstrom unit, right?
我们知道,它的尺寸大概是一埃，对吗？
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I am modeling them as billiard balls of a finite dimension.
我把它们想象成具有有限尺寸的台球。
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These are all isoelectronic, they all have the same electron configuration. And we can also think about going back to atomic size for a second.
这些都是等电子的，它们都有相同的电子排布，而,我们还可以再回想一下原子尺寸的概念。
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many of these ion channels have this size exclusion pore, it's a very important part of them.
很多离子通道也都有这样的具有尺寸排斥性的小孔，这是它们非常重要的组成部分。
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And when we talk about size, I'm again just going to say the stipulation we're not talking about an absolute classical concept here, but in general we're going to picture it being much further away from the nucleus as we move up in terms of n.
当我们说到尺寸时，我们只是说――,经典的绝对的概念，而是它大约,离原子核有多远。
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So, this is exactly how Rutherford did discover that these particles were present and made this new model for the atom that we now know has both a nucleus, and we know the size, and also has electrons.
他提出了一个,新的原子模型,这里面有一个原子核,和一个电子，原子核的尺寸是知道的。
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So, then we'll get to turn to a new kind of mechanics or quantum mechanics, which will in fact be able to describe what's happening on this very, very small size scale -- so on the atomic size scale on the order of nanometers or angstroms, very small particles.
然后我们要讲到一种,新的力学--量子力学,它可以解释,发生在很小尺度,大约是原子尺寸大小,也就是纳米或埃的量级。
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So, this is not to scale.
因此这不是说的尺寸。
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So, again, it is based on size, it's a little bit less intuitive than the idea of just straining out all of the potassium ions.
因此，这还是以尺寸为基础的，只是有点不够直观,与钾离子挤不进去的图像相比。
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And if we're talking about atomic radius, essentially we're talking about atomic size.
如果我们在讨论原子半径，实际上我们讨论的是原子的尺寸。
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The only thing that's different is that they're one down on the periodic table, potassium is down one row, so it's going to be a little bigger, but when we're thinking about size, it maybe does not seem that significant to talk about the size.
它们唯一的不同点,就在于其中一个在周期表的下面，钾在下一行，因此它要稍微大一些，但是当我们考虑尺寸的时候，似乎讨论尺寸的意义不大。
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So, not only did Professor Sayer, who's in the Chemistry Department who put together this contraption for all of you, not only did she magnify the size of these gold nuclei, but she actually had to smoosh all of these atoms closer together then they normally would be.
化学系的Sayer教授把这些玩意放到一起，她不仅把金原子核的,尺寸放大了,还把原子核的间距压缩了,事实上，如果原子核的尺寸有这么大,我们需要另一个大教室，放这个原子核。
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But instead in this chemistry course, I will just tell you the solutions to differential equations. And what we can do is we can start with some initial value of r, and here I write r being ten angstroms. That's a good approximation when we're talking about atoms because that's about the size of and atom.
但在这个课里，我会直接，告诉你们微分方程的解,我们可以给距离r一个初始值,我这里把r取10埃,当我们讨论原子时,这是一个很好的近似,因为原子的尺寸。
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