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1.77245... I don't want to knowwhat the square root of pi is.
VOA: standard.other
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There's absolutely no reason I couldn't have switched it around and said that instead the pi orbitals form between these atoms instead of those first atoms I showed.
我完全没有理由,不能把它转过来,现在π键在这些原子间,而不是我开始展示的那些原子间。
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So in order to rotate a double bond, you have to actually break the pi bond, so essentially what you're doing is breaking the double bond.
为了能够旋转双键，你必须打破一个π键，本质上我们要做的就是打破双键。
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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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Once you've got that, you can do minus 7 times a vector Just take the vector, multiply it by Pi and flip it over.
明白这点之后,你就可以计算-7乘以矢量,只需用 π 去乘以那个矢量,然后将其方向调转
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px 2py So we need to fill all the way up to the pi 2 p x, and the pi 2 p y.
我们需要填到。
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And the pi star orbitals result from any time you have destructive py interference from 2 p orbitals that are either the p x or the p y.
星轨道是由于2p轨道的相消干涉,不管是px还是。
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You can see that we have two unpaired electrons in this molecule here one in the pi 2 p x star, and one in the pi 2 p y star orbital.
你们可以看到我们这个,分子力有两个未配对电子,一个在π2px星，一个在π2py星轨道。
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z And what you need to remember is if the z 8 is equal to eight or greater, such as oxygen being the cut-off point, this sigma 2 p orbital is actually lower in energy than the pi 2 p orbitals, the molecular orbitals.
你们要记住如果,等于或者大于，就像O是分界点，这时sigma2p轨道,比π2p轨道能量更低。
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So let's fill it out in this way, 2p keeping in mind that we're going to fill sigma out the pi 2 p's before the sigma.
让我们这样填上去，记住我们先填π,轨道再填。
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So z equals 7 -- this is the cut-off where, in fact, the sigma orbital is going to be higher in energy than the pi 2 p orbitals.
所以z等于7-这是分界点，实际上，sigma轨道能量,要比π2p轨道高。
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So if we want to talk about the volume of that, we just talk about the surface area, which is 4 pi r squared, and we multiply that by the thickness d r.
如果我们要讨论它的体积，我们要用的是表面面积，也就是４πｒ的平方，乘以厚度ｄｒ
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So even though we see a nodal plane down the center, I just want to really point out that it's only when we have a nodal plane in the internuclear or the bond axis that we're calling that a pi orbital.
虽然在中间有个节面，我想要指出的是,只有节面在核间轴,或者键轴上时,我们才叫它π轨道。
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So if I try to rotate my 2 atoms, you see that I have to break that pi bond, because they need to be lined up so that the electron density can overlap.
如果我要试着转动两个原子，你会看到我必须要打破一个π键，因为他们需要连接起来,让那些电子能够重叠。
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Pi orbitals are a molecular orbital that have a nodal plane through the bond axis.
轨道是沿着键轴,有节面的分子轨道。
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px We'll call it either pi 2 p x, 2py if we're combining the x orbitals, or pi 2 p y.
我们叫它π,如果是x轨道组合的话，或者π
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Bohr said that the angular momentum, mvr where n is this integer counter h over 2 pi.
波尔提及到角动量，是被量化了的，mvr，is，quantized,这里的n等于一个整数乘以h除以2π
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So we're going to call this the sigma 2 p x star, or if we're talking about the 2 p y orbitals we'll call this the pi 2 p x star, and the pi 2 p y star.
我们叫这个sigma2px星，或者如果我们说的是π2py轨道的话,我们叫这个2px星，这个π2py星。
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But, of course, what you saw in recitation, and hopefully, what you can now think very quickly by looking at this, is that this is not the only configuration of pi bonds that we could have in benzene.
当然，你们在习题课看到过，你们通过看这个可以很快的想到，这不是苯环里,唯一的π键构型。
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These are the ones that are coming right out at you, so this is going to be on a second pi orbital.
它们朝向你们，所以这里有另一个π键。
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Square of the Planck constant times pi mass of the electron.
普朗克常量的平方,乘以π再乘电子的质量。
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And now the force, in its most general term / is q1q2 over 4 pi epsilon zero, which is the conversion factor r squared.
库仑力的最基本形式,就是，其中r是一个变量。
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r So the circumference is 2 pi r.
周长=2π
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And since we are not expecting the mass of the particle to change, what we really are saying is the uncertainty in its velocity times the uncertainty in its position is greater than the ratio of the Planck constant divided by 2 pi.
因为我们不期望,粒子质量发生变化，我们说的是,它速度的不确定度,乘以它位置的不确定度,比普朗克常量,除以2除以圆周率要大。
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So, we can do that by using this equation, which is for s orbitals is going to be equal to dr 4 pi r squared times the wave function squared, d r.
用这个方程,对于s轨道，径向概率分布,4πr的平方,乘以波函数的平方,这很容易理解。
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a perfectly spherical shell dr at some distance, thickness, d r, dr we talk about it as 4 pi r squared d r, so we just multiply that by the probability density.
在某个地方的完美球型壳层,厚度，我们把它叫做4πr平方，我们仅仅是把它,乘以概率密度。
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sigma That is one pi orbital. There is one sigma, one pi and there is a second pi, and that is how we are getting the triple bond.
那是一个pi轨道，有一个，一个pi，还有第二个pi轨道，这就是我们如何得到三线态的。
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n It takes discrete values, multiples of some integer n, and the multiplication factor is the ratio of the Planck constant divided by 2 pi where n takes one, two, three and so on.
这些离散的值乘以整数，乘积因子,是普朗克常数除以2π,其中n可以取1，2，3，等等。
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So that's two of our types of bonds in benzene, and we have one type left, that's going to actually be the double bond or the pi bond that So we can have one bond here between this carbon's p orbital and this carbon's p orbital.
这就是苯环里的两种键，我们还剩一种，那就是这些p轨道之间，形成的双键或者π键,我们可以在这个碳的p轨道,和这个碳的p轨道之间有个键。
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The reason that I wanted to point out this nodal plane here is because this is why it is called a pi orbital.
我指出这个节面的原因是因为,它就是为什么这个叫做π轨道的原因。
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