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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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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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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'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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It is the value of the radius of the ground state electron orbit in atomic hydrogen.
它就代表氢原子基态电子,的轨道半径。
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We can make some substitutions here using some of the derivation on the previous board which will give us the Planck constant divided by 2 pi mass of the electron times the Bohr radius.
在这里我们也可以,用我以前在黑板上写过的一些词来取代它,得到的是普朗克常数除以2π电子质量,再乘以波尔半径。
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What I just spent many lectures discussing is the fact that we can not know how far away an electron is from the nucleus, so we can't actually know the radius of a certain atom.
我花了这么多课时所讨论的正是我们,不可能知道电子离原子核有多远这一事实，因此我们不可能知道某个原子的半径。
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And again, we can define what that most probable radius is, that distance at which we're most likely to find an electron.
同样的，我们可以定义最可能距离，在这里找到电子的概率最大。
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So, essentially we're just breaking it up into two parts that can be separated, and the part that is only dealing with the radius, so it's only a function of the radius of the electron from the nucleus.
所以本质上我们把它写成,两个可分离的部分，这部分，只与半径有关，它仅仅是，电子,到核子距离的函数。
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What you see is that the radius changes with atomic number for constant electron number.
对于等电子数的粒子，离子半径随着,原子数的变化而变化。
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So because we're feeling a stronger attractive force from the nucleus, we're actually pulling that electron in closer, which means that the probability squared of where the electron is going to be is actually a smaller radius.
因为我们能感到来自原子核,的更强的吸引力，我们实际上会将电子拉的更近，那意味着电子运动的,概率半径是,事实上是一个更小的半径。
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So, basically what we're saying is if we take any shell that's at some distance away from the nucleus, we can think about what the probability is of finding an electron at that radius, and that's the definition we gave to the radial probability distribution.
本质上我们说的就是,如果我们在距离原子核,某处取一个壳层，我们可以考虑在这个半径处,发现电子的概率，这就是我们给出的,径向概率密度的定义。
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So, I want to contrast that with another concept that seemed to be opposing ideas, and that is thinking about not how far away the most probable radius is, but thinking about how close an electron can get to the nucleus if it's actually in that orbital.
我要将它和另外一个,看起来相反的概念相比较，我们不是考虑,最可能半径离原子核有多远，而是考虑如果电子在那个轨道上,能多接近原子核。
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And one common way to think about it, is to think about the value of r, or the radius, below which 90% of that electron density is going to be contained.
而通常的想法，是想象，r，的值，也就是半径的值，即有百分之九十的电子密度,都落在这个范围之内。
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n So the velocity is given by this product of the quantum number n Planck constant 2 pi mass of the electron time the radius of the orbit, which itself is a function of n.
速度是量子数,普朗克常数2π乘以轨道半径的值,它自身也是n的函数。
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