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We can graph out what this is where we're graphing the radial probability density as a function of the radius.
我们可以，画出它来,这是径向概率密度,作为半径的一个函数图。
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We can actually have any radius, but some radii just have much, much smaller probabilities of actually being significant or not.
非常非常小，以至于,无关紧要,我们今天。
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Sorry, said that wrong, p1 radius 1 and angle 2, 2 radians is a little bit more than pi half.
而是半径和角度的表示，在这个例子中点，并不对应这个点,它实际上对应的是。
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The radius of the orbit, the energy of the system and the velocity of the electron, I am just going to present you the solutions.
是轨道的半径，系统的能量,以及电子的速度，我接下来会给你们讲解其方程的解法。
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We are talking about probability, but what we're saying is that most probable radius is further away from the nucleus.
我们说的是概率，也就是说它的最可能半径,离原子核更远。
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Because what it tells is that we can figure out exactly what the radius of an electron and a nucleus are in a hydrogen atom.
我们可以,准确的算出,氢原子中,电子。
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So would you expect, therefore, as we go across a row for the atomic radius, to increase or to decrease? Good. OK, yes.
那么大家觉得，原子半径沿着某一行向右走，是会增大还是会减小呢？很好，不错，是的。
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We see that the radius is shorter, so that means that the nitrogen-nitrogen bond is going to be shorter.
我们看到这个距离更短，这就意味着,氮与氮之间的键应该更短。
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Instead, what people have done is come up with different ways to think about how they can define a radius.
而是，人们想出了其它方法,来定义半径。
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In other words, just want to know where the electron is somewhere within the shell radius of the ground state of atomic hydrogen anywhere.
换言之，我只是想知道,电子在哪,可以在氢原子基态下的半径,里面的任何地方。
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If its in Cartesian form I'll pass in an x and y and compute what a radius and angle is.
来得到的这个点,我都可以得到这个点的,全部的这种信息。
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We'll then take a turn to talking about the periodic table, we'll look at a bunch of periodic trends, including ionization energy, electron affinity, electronegativity and atomic radius.
然后我们再开始讲元素周期表，我们会看到很多周期性规律，比如电离能，电子亲和能，电负性以及原子半径。
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But luckily for us, there's a classical equation of motion that will, in fact, describe how the electron and nucleus change position or change their radius as a function of time.
但幸运的是，有一个,经典方程描述了电子和核子,位置或者它们直接的距离是,如何随时间变化的。
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But what's important is not where that most probable radius is when we're talking about the z effective it feels, what's more important is how close the electron actually can get the nucleus.
但重要的不是,最可能半径,当我们谈论它感到的有效电荷量的时候，更重要的是,电子实际上。
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How far you are away from the nucleus in terms of a radius, they don't depend at all on those two angles, theta they're independent of theta phi and they're independent of phi.
只和离核子的距离，也就是半径有关，它们和,另外两个角度无关，它们不决定于,也不决定于。
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So as we go down we're now adding electrons to further and further away shells, so what we're going to see is that the atomic radius is going to increase as we're going down the periodic table.
当我们向下走时,我们会将电子加在越来越远的壳层上，因此我们将看到原子半径,将随我们沿周期表向下走而增大。
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You just need to remember what's happening to z effective, which really tells us what's happening with all the trends, and once you know z effective, you can figure out, for example, what direction the atomic radius should be going into.
你只需要记住有效核电量的规律，实际上它会告诉我们所有的规律，只要你知道了有效核电量的规律，你就可以判断，比如，原子半径会向着哪个方向发展。
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And what we've been talking about with all of these properties are, of course, how can we figure out what that is for a certain atom by looking at the periodic table, so we want to think about the periodic trend for atomic radius.
对于我们讲过的这些性质，我们所讨论的一直都是,当然是，我们如何能够判断某一个原子的这些性质,通过观察周期表，因此我们需要思考一下原子半径的周期性规律。
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self y Notice what I also do here, I create self dot y, give it a value, and then, oh cool, I can also set up what's the radius and angle for this point, by just doing a little bit of work.
我创建了，然后给它赋值，然后，噢太酷了，通过做一点额外的工作,就可以得到点的半径和角度了，好，实际上如果。
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So what this means is that unlike s orbitals, they don't have the exact same shape at any radius from the nucleus.
这意味着和ｓ轨道不同，它们在离原子核不同距离处的形状不是完全一样的。
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Now, suppose in fact these weren't x and y glued together, these were radius and angle glued together.
我实际也说过了,我在这里操作的是，和这两个点。
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And immediately it should probably come into your head that we don't actually have an atomic radius that we can talk about, right?
一提到这点你就应该立刻想到,我们并没有一个真正的原子半径,可以讨论，对吗？
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The radius of the nucleus as compared to the radius of the entire atom is on the order of about one to 10,000.
原子核的半径,相对于整个原子的半径来说,是1比10000这个数量级。
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We can't define it as an exact radius in terms of the definition we might think of classically.
我们不能给它定义一个精确的半径,按照经典的图像来。
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If it's in polar form I passed in a radius and angle and I'll compute what the x- and y- value is.
以及半径和角度,但是现在是这样的,不管我是以哪种形式。
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So we haven't gotten to molecules yet, we're just talking about single atoms or single ions, but what's nice is just talking about this very straightforward principle of atomic radius.
我们还没有开始讲分子，我们仍然只是在讨论单个原子或离子，但它的好处在于可以讨论,这个关于原子半径的非常简单直接的原理。
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And I just want to point out here in terms of things that you're responsible for, you should know that the most probable radius for a 1 s hydrogen atom is equal a nought.
在这里,我想要指出的是，你们要知道氢原子１ｓ轨道,最可能距离等于ａ０
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So, keep that in mind when we're talking about atomic radius, I'm not suddenly changing my story and saying, yes, we do have a distinct radius.
因此，当我们讨论原子半径的时候要时刻记住这一点，我并不是在突然改变自己的说法，说是的，我们的确有一个准确的半径。
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In that case point p 1 doesn't correspond to this point, it actually corresponds to the point of radius 2 and angle 1, which is about here.
基本上也就是说这是第一个点1,这是第二个点，把它们的值加到一起,然后我就得到了目标点，好，这听起来挺不错的。
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