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And, in fact, if any electron comes in their midst, they'll capture it because the binding energy is so high.
事实上，如果电子从中间进来，它们会捕获它,因为束缚能是如此之大。
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So when you operate on the wave function, what you end up with is getting the binding energy of the electron, and the wave function back out.
所以当你将它作用于波函数时，你得到的是电子的结合能,和后面的波函数。
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And that makes sense, too, because the positive three pulling on minus one has a tighter binding energy than positive one pulling on minus one.
而这也是有意义的，因为+3和-1的相互吸引,产生了比+1和-1的吸引,更强的能量。
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And remember again, the binding energy physically is the negative of the ionization energy, and that's actually how you can experimentally check to see if this is actually correct.
电离能的负值，那个事实上是可以,通过实验来验证，它是否是对的,并且它等于负的。
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So now we can just take the negative of that binding energy here, and I've just rounded up here or 1 . 4 times 10 to the negative 19 joules.
等于4是第三激发态,现在我们可以取它结合能的负值,也就是1。4乘以10的负19次方。
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Right, because when we think of an energy diagram, that lowest spot there is going to have the lowest value of the binding energy or the most negative value of binding.
对因为当我们考虑,一个能量图时那里最低的点,是具有最低的结合能,或者最不活跃的结合能。
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So, for example, in a hydrogen atom, if you take the binding energy, the negative of that is going to be how much energy you have to put in to ionize the hydrogen atom.
例如在氢原子里面,如果你取一个结合能,它的负数就是。
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And an important thing to note is in terms of what that physically means, so physically the binding energy is just the negative of the ionization energy.
一个需要注意的很重要的事情,是它的物理意义，从物理角度来说结合能,仅仅是电离能的负数。
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So, what we can do is figure out what we would expect the binding energy of that electron to be in the case of this total shielding.
完全屏蔽的案例中,期望的电子结合,能再次记住,结合能物理上来说是。
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So if we can figure out the binding energy, we can also figure out how much energy we have to put into our atom in order to a eject or ionize an electron.
所以如果我们可以计算出结合能，我们也可以计算出,我们需要注入多少能量到原子中,去逐出或电离一个电子。
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When we talked about binding energy, we just had one quantum number.
当我们说到能量时，我们只要一个量子数。
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So we know that we're in the n equals 5 state, so we can find what the binding energy is here.
我们知道,我们在n等于5的态，我们可以找到结合能是多少。
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And that's going to be equal to the negative the binding energy of 2 s in b, in neutral boron.
它应该等于中性硼原子中,2，s，电子的束缚能的负值。
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What is the binding energy of the ground state electron in hydrogen?
氢在基态的情况下,它的电子结合能是多少？
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We're going to be looking at the solutions to the Schrodinger equation for a hydrogen atom, and specifically we'll be looking at the binding energy of the electron to the nucleus.
我们将研究下氢原子薛定谔方程的解,特别是电子和核子的结合能,我们将研究这部分。
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We looked at the wave functions, we know the other part of solving the Schrodinger equation is to solve for the binding energy of electrons to the nucleus, so let's take a look at those.
我们看过波函数，我们知道解,薛定谔方程的其他部分,就是解对于原子核的电子结合能，所以我们来看一看。
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And we know what that's equal to, this is something we've been over and over, ionization energy is simply equal to the negative of the binding energy.
而且你知道它等于什么，这是我们说过一遍又一遍的，电离能就等于,负的束缚能。
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And it should make sense where we got this from, because we know that the binding energy, if we're talking about a hydrogen atom, what is the binding energy equal to?
很容易理解，我们怎么得到这个的，因为我们知道，结合能，如果，对氢原子来说，结合能等于什么？
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And what we call the binding energy is this is what we saw on the last slide.
我们所说的束缚能,这个我们在上一张幻灯片中已经见过了。
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We know that binding energy is always negative, ionization energy is always positive.
我们知道结合能，总是负的，电离能总是正的。
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The ionization energy, of course, is just the negative of the binding energy.
电离能，我们知道也就是,负的结合能。
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And we can look at precisely why that is by looking at the equations for the energy levels for a hydrogen atom versus the multi-electron atom. So, for a hydrogen atom, and actually for any one electron atom at all, this is our energy or our binding energy.
而且我们可以精确地看看,为什么是这样的,通过看对于氢原子和,多电子原子能级的方程所以对于氢原子，事实上对于任何一个电子，这是我们的能量或者我们的结合能。
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We've got a lot of constants in this solution to the hydrogen atom, and we know what most of these mean. But remember that this whole term in green here is what is going to be equal to that binding energy between the nucleus of a hydrogen atom and the electron.
在这个解中有很多常数,其中大部分我们,都知道它们代表的意思,但记住是这整个绿色的部分,等于核子和电子的结合能。
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And if we do that calculation, what we find out is that the binding energy, in this case where we have no shielding, 72× is negative 8 . 7 2 times 10 to So, let's compare what we've just seen as our two extremes.
我们会发现结合，能在这个情况中，没有屏蔽，等于-8。,所以我们来对比一下,我们在两个极端的案例中看到了什么。
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it's an easy calculation -- we're just taking the negative of the binding energy, again that makes sense, because it's this difference in energy here. So what we get is that the binding energy, when it's negative, the ionization energy is 5 . 4 5 times 10 to the negative 19 joules.
这个计算很简单-我们,只需要取结合能的负值,同样这很容易理解，因为这就是这的能量差,所以我们得到的就是结合能,当它取负值，电离能就是5。45乘以。
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And we know that n describes the total energy, that total binding energy of the electron, so the total energy is going to be equal to potential energy plus kinetic energy.
我们知道，n是描述总能量的，电子总的结合能，所以总能量，等于,势能加动能。
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This e term here is the energy, or in our case when we talk about an electron in a hydrogen atom, for example, the binding energy of that electron to the nucleus.
这里的“E“是指能量，或者在我们谈论一个,氢原子的电子时，举例来说，是电子对于原子核的结合能。
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So, what we call this is the third ionization energy, or the negative of the binding energy, again of the 2 s orbital, but now it's in boron plus 2 to we're starting with.
那么我们称它为第三电离能，或者负的束缚能，还是，2，s，轨道的，但现在我们是从正二价硼离子开始的。
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And again, this is just the negative, the binding energy, when we're talking about the 2 p orbital.
再说一遍，这就是负的束缚能，当我们考虑，2，p，轨道的时候。
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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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