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"And,the President's budget for 2009 in the recovery act had the largest increase for R&D that we have seen in recent years."
VOA: standard.2009.08.31
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And we reasoned that these two eventually reach some kind of an equilibrium separation which we are using lowercase r to represent.
我们推导,这两个最终能达到,某种平衡分离,我们用小写的r代表。
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and the same for favour, they spell f-a-v-o-r, we put u in it,
同样地，对于发烧这个单词，他们拼写成f-a-v-o-r，我们要加一个u在里面，
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We will always have r equals zero in these radial probability distribution graphs, and we can think about why that is.
在这些径向概率分布图里,总有ｒ等于０处，我们可以考虑为什么会这样。
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So instead of v bar, we write p v bar minus b, equal r t.
现在考虑，这些气体分子之间。
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And we can find r naught by looking for the minimum.
我们可以通过寻找最小值得到r圈。
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What we do is we take the interest rate, which I'll call r, and plug it into a formula, which I didn't actually do the arithmetic to their number.
我们只需将利率r,代入等式中,虽然我没有代入数字验证过...
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So under the R group there we've got positive, happy, secure.
组下面我们写了积极,愉悦,安详
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We've got one vector which is R.
我们已有的一个矢量,位矢 R
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And when we define that as r being equal to zero, essentially we're multiplying the probability density by zero.
当我们定义ｒ等于０处，事实上是把概率密度乘以０．
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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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We're saying the probability of from the nucleus in some very thin shell that we describe by d r.
某一非常薄的壳层dr内,一个原子的概率,你想一个壳层时。
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And that's what we label as r sub m p, or your most probable radius.
或者最可能半径，这是你找到。
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So that's why we have this zero point here, and just to point out again and again and again, it's not a radial node, it's just a point where we're starting our graph, because we're multiplying it by r equals zero.
这就是为什么在这里有个零点，我需要再三强调，这不是径向零点，他只是我们画图的起始处，因为我们用ｒ等于０乘以它。
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Were going to make it for a mole of gas, T1 so it's R times T1, V and then we'll have dV over V.
假设是有一摩尔气体，那么就是R乘以，然后有dv除以。
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So, what we can do to actually get a probability instead of a probability density that we're talking about is to take the wave function squared, which we know is probability density, and multiply it by the volume of that very, very thin spherical shell that we're talking about at distance r.
我们能得到一个概率,而不是概率密度的方法,就是取波函数的平方，也就是概率密度，然后把它乘以一个在ｒ处的,非常非常小的,壳层体积。
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When we're talking about r for internuclear distance, we're talking about the distance between two different nuclei in a bond, in a covalent bond.
当我们说，r，代表的是核间距的时候，我们讨论的是一个距离,在一个键--一个共价键的两端的原子核之间的距离。
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And then we have r, which is simply the distance between the two charges.
和两者距离的成负相关，我们把这种表述简化，成负e的平方除以4π
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dE/dr=0 We take dE by dr equals zero at r equals r naught.
当r等于r圈时。
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So, let's say we start off at the distance being ten angstroms. We can plug that into this differential equation that we'll have and solve it and what we find out is that r actually goes to zero at a time that's equal to 10 to the negative 10 seconds.
也就大约是这么多,所以我们取初始值10埃,我们把它代入到,这个微分方程解它,可以发现，r在10的,负10次方秒内就衰减到零了。
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We found that it's R log V2 over V1.
这是路径A，我们已经得到它。
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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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We differentiate dE by dr.
用E对r求导。
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RT2 So it's R T2, right, now we're at a lower temperature times log the log of V4 over V3.
等于，这时温度比刚才低,乘以。
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And we can simplify this expression as saying negative e squared over 4 pi, epsilon nought r squared. Epsilon nought is a constant, it's something you might see in physics as well.
也会遇到它,在这里，你可以就把它,理解为一个转换系数,我们需要做的。
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r- So we could just say r plus plus r minus gives you r naught.
因此我们能够说r+加上,得到r圈。
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We take this Cv and put in the exponent here R right. And we put this R up in the exponent here.
我们把这个Cv提出来,放在这里的指数上，好吧？然后把。
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And we call that most probable radius r sub m p, or most probable radius.
我们叫它ｒ小标ｍｐ,或者最可能半径。
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So, you remember from last time radial nodes are values of r at which the wave function and wave function squared are zero, so the difference is now we're just talking about the angular part of the wave function.
你们记得上次说径向节点在,波函数和波函数的平方,等于零的ｒ的处，现在的区别是我们讨论的是,角向波函数。
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R And we abbreviate that by calling it r, l by two quantum numbers, and an l as a function of little r, radius.
我们把它简称为，两个指定的量子数n和，它是半径小r的函数。
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