-
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
-
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。
-
pV=RT p plus a over v bar squared times v bar minus b equals r t. All right if you take a equal to zero, these are the two parameters, a and b. If you take those two equal to zero you have p v is equal to r t.
我们就回到,也就是理想气体,状态方程,下面我们来看看,这个方程。
-
And now the force, in its most general term / is q1q2 over 4 pi epsilon zero, which is the conversion factor r squared.
库仑力的最基本形式,就是，其中r是一个变量。
-
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。
-
So the integral of one 1/r over r squared gives you one over r.
所以就有了,我们在上面提到的1/r^2和。
-
Force goes as one over r squared.
力和1/r^2成正比。
-
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。
-
So, the number of nuclei, 119 if we were to sit and count these as well, is 119. So, we'll multiply that by just pi, r squared, to get that cross-section, and divide all of that by 1 . 39 meters squared.
如果你们数的话，原子核的数是，我们用它乘以πr的平方，得到横截面积，除以1。39平方米。
-
So kind of that strange cursive r, and our n final is 2, R so 1 over 2 squared minus n initial, so 1 over 3 squared.
因为我们可以在这里用到它，这个有点奇怪的花体。
-
And so, you know from your Newtonian mechanics, as you were learning in 8.01, the dynamic force here mv^2/r is mv squared over r.
在8。01节对牛顿动力学系统的学习中，我们可以知道这里的运动受力,就是。
-
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。
-
And we plug in our values and end up with mv squared mv^2/r-Ze^2/ over r minus Ze squared over And I am going to call this equation two.
我们最后的结果,就是,我把这称为方程式二。
-
So instead of being equal to negative z squared, now we're equal to negative z effective squared times r h all over n squared.
这里不再等于-z的平方，现在我们等于-有效的z的平方,乘以RH除以n的平方。
-
And that's going to be equal to negative z effective squared times r h over n squared.
有效的z的平方,乘以RH除以n的平方。
-
e The charge on the anion times minus e, so there is the minus e squared, 0R0 and divided by 4 pi epsilon zero r naught, because now I am evaluating this function at r naught, one minus one over n where n is the Born exponent.
阴离子的电荷乘以，因此会有-e的频繁，除以4πε,因为现在我用r圈评估这个函数，1-1/n，n是波恩指数。
-
So we know that we can relate to z effective to the actual energy level of each of those orbitals, and we can do that using this equation here where it's negative z effective squared r h over n squared, we're going to see that again and again.
我们知道我们可以将有效电荷量与,每个轨道的实际能级联系起来，我们可以使用方程去解它,乘以RH除以n的平方,它等于负的有效电荷量的平方,我们将会一次又一次的看到它。
-
I know the energy in this first pair would equal -e^2 That is just going to equal minus e squared over 4 pi epsilon zero r naught.
我们明白第一对的能量将会等于,等于,/4πε0，R圈。
-
So the square root of n squared r e over r h.
这里的n值是什么呢？
-
If you get one over R squared, it'll be a little steeper.
如果你用1除以R的平方，它会变得稍微陡峭一些。
-
So, we can get from these energy differences to frequency h by frequency is equal to r sub h over Planck's constant 1 times 1 over n final squared minus 1 over n initial squared.
所以我们通过不同能量,得到不同频率，频率等于R下标,除以普朗克常数乘以1除以n末的平方减去。
-
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。
-
We also know how to figure out the energy of this orbital, and we know how to figure out the energy using this formula here, which was the binding energy, -Rh which is negative r h, we can plug it in because n equals 1, so over 1 squared, and the actual energy is here.
我们知道如何算出,这个轨道的能级，而且我们知道如何,用这个公式,算出能量，也即是结合能，等于，我们把n等于1代进来，所以除以1的平方，这就是能量。
应用推荐