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"There have been some studies showing that if you give pregnant women 4,000 units of vitamin D a day, their rates of complications in pregnancy are much decreased."
VOA: standard.2010.05.28
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And if someone said, it's 4%, you'd say, well that's kind of meager, I want a better dividend than that.
如果他说,是4%,你会觉得少,我想要更高的股利
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So if we want to talk about the volume of that, we just talk about the surface area, which is 4 pi r squared, and we multiply that by the thickness d r.
如果我们要讨论它的体积，我们要用的是表面面积，也就是４πｒ的平方，乘以厚度ｄｒ
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And so in theory after just 2 or 3 steps you were in order of magnitude farther along in this counting process than I would be because I'd still be on person literally 3 or 4.
因此从理论上说,经过这样短短的两三个步骤,你们就有了分级次序，比我数数快多了,因为我才数到第三四个人。
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It's above what we'd like; we'd like it to be more like 2% 4% is high.
这超过了我们的偏好；,我们希望它在2%到4%的范围内。
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So I could refer to the 4' carbon and you'd know I'd mean this one, or the 2' carbon you'd know I mean this one.
所以当我说,4'碳的时候你就知道是讲到哪个碳,2'碳的话就是指的这里
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And often the president would hear 2 and 4, 5 and he'd say 5.
通常总统听到了2和，但他会说。
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Again I should have said first, index 0, the first one. I can similarly go in and say I'd like all the things between index 2 and index 4. And again, remember what a b c that does. Index 2 says start a 0. 1, 2. So a, b, c.
我还是要说一遍，索引为0的元素，是第一个元素，我可以要求返回索引,2和4之前的所有元素，请记住2,是从0开始的,那么0，1，2对应的是。
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d1 2 3 And we can do that just going along, 3 d 1, 2 3, and the problem comes when we get to chromium here, which is instead of what we would expect, 4s23d4 we might expect to see 4 s 2, 3 d 4.
我们能做的就是继续，问题出现了,当我们来到铬元素时，它不是我们预期的那样，我们可能预期。
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s1 So for the fourth period, now we're into the 4 s 1 3d for potassium here. And what we notice when we get to the third element in 4s2 and the fourth period is 3d that we go 4 s 2 and then we're back to the 3 d's.
对于第四周期到现在我们来到钾的1,然后我们返回到,我们注意到当我们看到第三个元素,第四周期我们来到,然后我们返回到。
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We'd look over 4-month calendar.
我们会看整个四个月。
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So what I want to point out is 3d2 what we said now is that the 3 d 2 is actually lower in energy, so if we were to rewrite this in terms of what the actual energy order is, 3d2 4s2 we should instead write it 3 d 2, 4 s 2.
所以我们想指出的是,我们现在所说的是,实际上能量比较低，所以如果我们重新的,写出实际的能量顺序，我们应该写出。
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s13d5 What we see is that instead it's 4 s 1, and 3 d 5.
而我们看到的是。
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s So, we would actually take an electron out of the s, 3 d 3 4 s 1 which gives us 3 d 3 and then 4 s 1.
轨道，The，s。,因此，我们应该拿走s，轨道上的一个电子，然后得到。
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a perfectly spherical shell dr at some distance, thickness, d r, dr we talk about it as 4 pi r squared d r, so we just multiply that by the probability density.
在某个地方的完美球型壳层,厚度，我们把它叫做4πr平方，我们仅仅是把它,乘以概率密度。
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So, we can do that by using this equation, which is for s orbitals is going to be equal to dr 4 pi r squared times the wave function squared, d r.
用这个方程,对于s轨道，径向概率分布,4πr的平方,乘以波函数的平方,这很容易理解。
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So what we know is that these 3 d orbitals are higher in energy than 4 s orbitals, so I've written the energy of the orbital here for potassium and for calcium.
我们所知道的是,3d轨道能量,比4s轨道能量高，所以我写出了,钾和钙的轨道能量。
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So, for example, if we needed to figure out the electron configuration for titanium, 4s2 it would just be argon then 4 s 2, 3d2 and then we would fill in the 3 d 2.
所以举个例子,如果我们需要解出钛的电子构型，它会是Ar然后，然后我们填充。
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So if we were to write this in terms of energy, 4 s 2 we would actually have to rewrite it has 3 d 3, and then 4 s 2.
因此，如果我们按照能量的顺序来写的话，我们应该先写，3，d，3，然后才是。
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So if you look at the energy diagram, what we see is that the 4 s orbitals are they're just ever so slightly lower in energy than the 3 d orbitals.
如果你看能量图，我们看到的是4s轨道,他们仅仅比3d轨道,能量低一点点。
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d 3 Then 4 s 2 and 3 d 3.
然后是，4，s，2，与。
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I don't care how you do it on exams or on problem sets, but you do need to be aware that the 3 d once filled is lower in energy than the 4 s, and the reason you need to be aware of that is if you're asked for the electron configuration now of the titanium ion.
我不关心你们在考试或者,问题集中如何做它，但是你们的确需要知道3d一旦被填充,它的能量是小于4s的，你们需要知道这个的原因,是如果你现在被要求,写出钛离子的电子构型。
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s But it just turns out that the 4 s is so low in energy that it actually surpasses the 3 d, because we know the 3 d is going to be pretty high in terms of the three shell, and the 4 s is going to be the lowest interms of the 4 shell, and it turns out that we need to fill up the 4 s 4s before we fill in the 3 d.
但是结果是,能量较低,4s是第四层最低的，因为我们知道3d在第三层,是非常高的，4s是第四层,最低的，结果是我们在填充3d之前,需要先填充。
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You wouldn't be expected to be able to guess that this would happen, because using any kind of simple theory, we would, in fact, predict that this would not be the case, but what we find experimentally is that it's more stable to have half filled d orbital than to have a 4 s 2, and a 3 d 4.
你们不用预期有能力,猜出这个会发生，因为使用任一种简单的理论，我们事实上可以预测不会是那种情况，但是我们在实验中发现的,是半填充d轨道比,4s23d4更加稳定。
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