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。
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。
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。
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。
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。
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。
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。
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。
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。
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。
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。
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。
At first it might be counter-intuitive because we know the probability density at the nucleus is the greatest.
起初我们觉得这和直观感觉很不相符,因为我们知道在原子核,出的概率密度是最高的。
There's some probability that it can get very, very close the nucleus, and that probability is actually substantial.
有一定的概率,它能非常非常接近原子核,这个概率是相当大的。
And so we have a positive charge in the nucleus which is given by the number of protons.
在原子核上,有很多质子聚集而形成的正电荷。
And we know that it's electron density between the nuclei that holds two atoms together in a bond.
我们知道是两个原子核之间的,电子密度保持两个原子在一起成键的。
It is about 10,000 to one, the ratio 10000 of the nuclear dimension to the entire atomic dimension.
原子核和整个原子的大小比例,约为1:
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。
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。
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。
And we know as we go across a row in the periodic table, what's happening is that z effective or the effective pull on the nucleus is increasing.
而我们知道沿着周期表的某一行向右看,有效核电量,或者说原子核的有效引力是在逐渐增大的。
And we can also talk about the bond length, so we might be interested in what the bond length is, what the distance between these two nuclei are.
另外一点就是键长,我们对键的长度也感兴趣,也就是两个原子核之间的距离。
When we were talking about constructive interference, we had more electron density in between the 2 nuclei.
当我们讨论相长干涉的时候,在两个原子核之间有更多的电子密度。
So, remember when we talk about Coulomb force, what's holding the nucleus and the electron together, there's 2 things we need to think about.
还记得我们在讨论库仑力的时候,提到是什么将原子核与电子束缚在一起时,有两点需要考虑。
That is why we don't worry about the motion of the nucleus 1 because the ratio of mass is about 2,000 to one.
这就解释了为什么我们不担心,原子核运动起来,因为原子核和电子的质量比约为2000:
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。
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。
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。
So, here we have the area of the nuclei we'll figure out adding those all together versus the space of all of the atoms put together.
有原子核的面积,通过除以所有原子的,总面积。
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