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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 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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Cv+R=Cp Cv is equal, oh Cv plus R is equal to Cp it's a relationship that we had up here that we wanted to prove.
我们就得到了,我们一开始,想要证明的。
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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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We notice that the value of E at r naught is negative, as it should be. It's a negative number.
我们主要到在r圈时E的值为负，和它本来的值一致，是一个负数。
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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 we know it's moving on a circle of radius r.
因此这个质点始终在做半径为 r 的圆周运动
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We can use the Coulomb force law to explain this where we can describe the force as a function of r.
我们用库伦定律解释它,力作为距离r的函数,让我们考虑一下。
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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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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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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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l But now we need to talk about l and m as well. So now when we talk about a ground state in terms of wave function, we need to talk about the wave function of 1, 0, 0, and again, as a function of r, theta and phi.
但我们现在需要讨论,和m，现在当我们讨论,波函数的基态时，我们讨论的，是1，0，0的波函数，同样的，它也是r，theta和phi的函数。
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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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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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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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If you are describing a particle with location R, the vector we use typically to locate a particle, R then R is just i times x + j times y, because you all know that's x and that's y.
如果你要描述一个位移为 R 的质点,这个矢量一般用表示质点 R 的位移,R 可表示为 i ? x + j ? y,显然你们都知道这段是 x,那段是 y
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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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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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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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