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We have 266, as some of you might know who saw me counting ping-pong balls the other day in office hours.
看到了这些发泡胶球事实上,可以当作单层金原子核,我们有266个乒乓球。
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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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We cannot do anything about protons, they are buried in the nucleus, but we can add or subtract electrons.
我们不能改变质子，它们埋藏在原子核内，但是我们能够增加或减少电子。
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And then the potential energy, the energy is stored here due to the coulombic force of attraction between the electron and the nucleus.
然后说势能,位能其实就是,由电子和原子核之间的库仑引力而形成的能量。
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It was a classical model, right, so we could say the electron is exactly this far away from the nucleus.
这是个经典模型，对吧，我们说电子离,原子核就是这么远。
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So I will take into account it that there is some contribution of both the nucleus and the electron.
所以我将考虑,那是原子核与电子,共同作用的结果。
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And so the other thing that we consider is the nucleus as being stationary.
接下来我们讲的是,原子核是静止的。
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So it's trigonal because we have these three atoms that are bound to the central atom here, and if you picture it, it's actually shaped like a pyramid.
这里三角形是因为,我们有3个原子核中心原子成键，如果你画它，它就是金字塔形的。
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And let's say our second electron now is really far away, such that it's actually not going to shield any of the nuclear charge at all from that first electron.
距离原子核非常非常近,我们说第二个电子处于非常远的位置,这样它不会对第一个电子,感受到的来自原子核的电荷量有任何屏蔽作用,我们最后要说的是。
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The reason is because the predominant force at this point is going to be the attraction that's being felt between the nuclei and the electrons in each of the atoms.
这是因为这时候最主要的力,是吸引力，它来自于,其中一个原子的电子与另外一个原子的原子核之间。
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So, the size still for an s orbital is larger than for a d orbital, but what we say is that an s electron can actually penetrate closer to the nucleus.
轨道的尺寸比,ｐ轨道还是要大，但我们说的是ｓ轨道可以,穿透到更接近原子核的地方。
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Right, this makes a lot of sense because if the entire atom was made up of nuclei, then we would have 100% probability of hitting one of these nuclei and having things bounce back.
因为如果整个原子,都是原子核，那我们就有100%概率,撞到一个原子核并被弹回来,所以如果我们。
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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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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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So if you have some charge in the nucleus, but you also have repulsion with another electron, the net attractive charge that a given electron going to feel is actually less than that total charge in the nucleus.
所以如果在原子核中，有一些电荷但是你也有来自，另一个电子的排斥力,那么一个给定电子的,吸引电荷感觉到的事实上,小于原子核中的总电荷。
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So, if I kind of circle where the probability gets somewhat substantial here, you can see we're much closer to the nucleus at the s orbital than we are for the p, then when we are for the d.
我把概率,很大的地方圈出来，你们可以看到在ｓ轨道上,比ｐ轨道更接近原子核，最远是ｄ轨道。
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The first is this the z effective, or how much charge is actually in the nucleus that's felt, Z or the I guess we would say the z, how much the charge is on the nucleus that holds it close together.
第一个是有效核电量，或者说实际感受到的核电荷量，又或者我想我可以说就是，使它们保持在一起的,原子核的电荷量。
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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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So let's take two cases of shielding if we're talking about, for example, the helium, a helium nucleus or a helium atom.
所以我们来对屏蔽举两个例子,如果我们在讨论氦，举例来说一个氦原子核或者氦原子。
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Remember in the ion, we're going to have less electrons around to counteract the pull from the nucleus.
还记得在这个离子中，在原子核周围,抵消它吸引力的电子更少。
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It is no longer tethered to the nucleus so there is no energy stored in the system.
它已经不再受原子核的吸引,所以这个系统中没有能量储存了。
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So you can see that this is non-bonding, this is even worse than non-bonding, it's anti-bonding, because we're actually getting rid of electron density between the two nuclei.
所以你可以看到这是不成键的，它甚至比不成键还糟糕，它是反键，因为我们实际上是去掉了,两个原子核之间的电子。
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So again, this is an anti-bonding orbital, and what you see is that there is now less electron density between the two nuclei than there was when you had non-bonding.
同样的，这是反键轨道，你们看到当你有反键轨道的时候,两个原子核中间的电子密度更小了。
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We are expecting to see that it decreases because it's feeling a stronger pull, all the electrons are being pulled in closer to the nucleus, so that atomic size is going to get smaller.
我们将看到它是减小的,因为电子会感受到越来越强的吸引力，所有的电子将会被原子核拉得越来越近，所以原子半径将越来越小。
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If we have a higher z effective, it's pulled in tighter, we have to put in more energy in order to eject an electron, so it turns out that that's why case 2 is actually the lowest energy that we need to put in.
而如果有效核电量更高，原子核的束缚也就更紧，我们不得不输入更多的能量来打出一个电子，这就是第二种情况,所需要输入的,能量更少的原因。
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And the reason that they're the least sheilded is because they can get closest to the nucleus, so we can think of them as not getting blocked by a bunch of other electron, because there's some probability that they can actually work their way all the way in to the nucleus.
它们最不容易被屏蔽的原因,是因为他们可以更加接近原子，所以我们可以认为它们,最不容易被其它原子阻挡住，因为它们有一定的概率,离原子核非常近。
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It turns out, and we're going to get the idea of shielding, so it's not going to actually +18 feel that full plus 18, but it'll feel a whole lot more than it will just feel in terms of a hydrogen atom where we only have a nuclear charge of one.
结果是我们会有,屏蔽的想法,所以它不会是完整的，但是它会比原子核电荷量,吸引力要大很多,只有1的氢原子的。
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It's not going to be a backscatter event if your ping-pong ball hits the frame or these strings, or the top part.
打到原子核了就是背散射,如果打到框上。
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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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