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If you solve for r, you will end up with this.
解决了半径的问题，就基本结束了。
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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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Mathematically, it's done by taking the expression for R and differentiating everything in sight that can be differentiated as vector t.
从数学上看是这样的,写出 R 的表达式,并对所有可以进行矢量微分的部分,对时间 t 求微商
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Let me just solve this for--let's solve x1 for r.
现在我们先解出用r表示x1的关系等式。
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P dV is equal to R dT. pV = RT for 1 mole, pdV=RdT so I just take dV here.
对等压过程，那么。
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You might want to say in the real world, if you go to a movie theater for this R-rated movie, "Are you 18 and over or are you with a parent?"
在现实世界中，你可能想说，如果你去电影院看R级电影，“你有18岁吗？,或者你跟随你的父母亲来的吗？“
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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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If you think of two towns down here, Brive,b-r-i-v-e,famous for its rugby, and Tulle,t-u-l-l-e,which is a capital.
如果你可以想起来这儿的两个城镇,布瑞福,b-r-i-v-e,以英式橄榄球运动而负有盛名,图勒,t-u-l-l-e,是一个省的首府
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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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It was found in strain R, a particular strain of E.coli, and it was the first one found, There's a nomenclature that's evolved for this.
酶被发现于R菌株,大肠杆菌中一种特别的菌株,又是被发现的第一种内切酶,有一种专门为此制定的命名法
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It's true for any gas, and if I remove this limit here, r t is equal to p v bar, I'm going to call that an ideal gas.
这样的气体被称作理想气体,这就是理想气体的性质，理想气体的涵义是什么？
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Generally, if it pays c dollars for every period, the present value is c/r.
推广开来,如果在每段时期内支付c美元,那么它的现值就是c/r
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We call that a node, r and a node, more specifically, is any value of either r, the radius, or the two angles for 0 which the wave function, and that also means the wave function 0 squared or the probability density, is going to be equal to zero.
节点就是指对，于任何半径，或者，两个角度,波函数等于，这也意味着波函数的平方或者概率密度,等于，我们可以看到在1s轨道里。
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It just turns out that if you put the v^2 and you put the r, and r is 93 million miles, you will find the acceleration is small enough for us to ignore.
这样的话,如果你把 v^2 和 r 代进去,r 是 9300 万英里,你会发现加速度小得足以被忽略
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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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Then we go negative and we go through zero again, which correlates to the second area of zero, that shows up also in our probability density plot, and then we're positive again 0 and approach zero as we go to infinity for r.
并且再次经过,这和，第二块等于0的区域相关联,这也在,我们的概率密度图里反映出来了，然后它又成了正的,并且当r趋于无穷时它趋于。
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If you go and work that out, log2 log of two and you have two log two, by math you can show that for the line r series m 2*log2 is equal to two natural log of two, which is 1 1.386 which is greater than one.
如果你把它计算出来，这二者的对数，你会得到2个，通过数学，你会得到第r列，第m个值,等于,也就是1。386，这大于。
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g has to be less than r for this to make sense because if g--if it's growing faster than the rate of interest, then this infinite series will not converge and the value would be infinite.
必须小于r才行得通,因为如果g比利率涨的还快,那么这个无穷序列就不会收敛,价值就是无穷了
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We'll introduce in the next course angular nodes, but today we're just going to be talking about radial nodes, psi and a radial node is a value for r at which psi, and therefore, 0 also the probability psi squared is going to be equal to zero.
将会介绍角节点,但我们今天讲的是，径向节点，径向节点就是指，对于某个r的值,当然，也包括psi的平方，等于,当我们说到s轨道时。
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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 we have the operationon the wave function in terms of r, theta, and phi and remember this e is just our binding energy for the electron, and we get back out this wave function.
我们用r，θ，φ来表示,将算符作用于波函数,而且记住e仅仅是电子结合能，然后后面加上波函数。
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