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And Pauli says no two electrons in a given system can have the entire set of quantum numbers identical.
而泡利认为在一个给定的系统内,没有两个电子有完全相同的量子数。
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He has two electrons here with the same set of quantum numbers. B but these are two separate hydrogen atoms.
因为我写了两个量子数,一样的电子,但这是在两个不同原子中啊。
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what three quantum numbers tell us, versus what the fourth quantum number can fill in for us in terms of information.
三个量子数和,四个量子数告诉我们的信息。
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OK, great. So, most of you recognize that there are four different possibilities of there's four different electrons that can have those two quantum numbers.
Ｋ，大部分都认为,有４个不同的可能,有四个不同的电子可以有,这两个量子数。
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So if we're talking about the fourth excited state, and we talk instead about principle quantum numbers, what principle quantum number corresponds to the fourth excited state of a hydrogen atom.
如果我们说的是,第四激发态，我们用,主量子数来描述，哪个主量子数对应了,氢原子的第四激发态？
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So let's go to a second clicker question here and try one more. So why don't you tell me how many possible orbitals you can have in a single atom that have the following two quantum numbers?
让我们来看下一道题目,你们来告诉我,有多少个可能的轨道,含有这些量子数呢？
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Yeah. So we have two orbitals, or four electrons that can have that set of quantum numbers.
嗯，有我们有两个轨道，也就是４个电子可以有这套量子数。
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So now we're just counting up our orbitals, an orbital is completely described by the 3 quantum numbers.
所以现在我们只要把这些轨道加起来，一个轨道是由３个量子数完全确定的。
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The reason there are three quantum numbers is we're describing an orbital in three dimensions, so it makes sense that we would need to describe in terms of three different quantum numbers.
我们需要，3个量子数的原因,是因为我们描述的是一个，三维的轨道，所以我们需要，3个不同的量子数,来描述它。
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So there's two different orbitals that can have these three quantum numbers, but if we're talking about electrons, we can also talk about m sub s, so if we have two orbitals, how many electrons can we have total?
所以有两个轨道可以有,这三个量子数，但如果我们讲的是电子，我们还要考虑ｍ小标ｓ,如果我们有两个轨道，一共有多少个电子呢？
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All right, so hopefully if you see any other combination of quantum numbers, for example, if it doesn't quickly come to you how many orbitals you have, you can actually try to write out all the possible orbitals and that should get you started.
所以希望你们如果遇到,任何其它的量子数组合的问题，如果你们不能马上想到有多少个轨道，可以试着先写出所有的轨道,这是个不错的切入点。
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So each electron has a distinct set of quantum numbers, the first important idea.
每个电子的量子数,是不尽不同的，对于这第一个重要观点。
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- The same place is that energy is a function of these four quantum numbers.
它就是这个结论,能量是这四个量子数的机能显示。
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So you'll notice in your problem-set, sometimes you're asked for a number of orbitals with a set of quantum numbers, sometimes you're asked for a number of electrons for a set of quantum numbers.
希望你们在做习题的时候注意到，有时候问的是拥有,一套量子数的轨道数，有时候问的是拥有一套,量子数的电子数。
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And I just want to point out that now we have these three quantum numbers.
我想指出的是,现在我们有了，这3个量子数。
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How many different orbitals can you have that have those two quantum numbers in them?
有多少个轨道是,含有这两个量子数的？
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That makes sense because we know that every single electron has to have its own distinct set of four quantum numbers, the only way that we can do that is to have a maximum of two spins in any single orbital or two electrons per orbital.
那个讲得通,因为我们知道每一个电子,都有它自己独特的量子数,我们能做的唯一方式是,在任一单个轨道中最多有两个自旋电子,或者每个轨道有两个电子。
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And we also, when we solved or we looked at the solution to that Schrodinger equation, what we saw was that we actually needed three different quantum numbers to fully describe the wave function of a hydrogen atom or to fully describe an orbital.
此外，当我们解波函数,或者考虑薛定谔方程的结果时，我们看到的确３个不同的量子数,完全刻画了氢原子,的波函数或者说轨道。
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Remember, we need those three quantum numbers to completely describe the orbital.
要知道，我们需要三个量子数,才能完全描述一个轨道。
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R And we abbreviate that by calling it r, l by two quantum numbers, and an l as a function of little r, radius.
我们把它简称为，两个指定的量子数n和，它是半径小r的函数。
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So we can completely describe an orbital with just using three quantum numbers, but we have this fourth quantum number that describes something about the electron that's required for now a complete description of the electron, and that's the idea of spin.
所以我们可以用３个,量子数完全刻画轨道，但我们有这第四个量子数,来完整的,描述电子，这就是自旋的概念。
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So, those are our three quantum numbers.
这就是，3个量子数。
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Pauli So, here, Pauli came out on top, we say, and he's known for the Pauli exclusion principle, which tells us that no two electrons in the same atom can have the same four quantum numbers.
在这里是，他因为Pauli不相容原理而出名，这个原理是说同一个原子中的两个电子,不能有相同的第四量子数。
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And in order to label the various orbitals, as he called them, m he introduced two more quantum numbers, l and m.
为了给他所说的不同的轨道，标号，他又另外引进了两个量子数，l和。
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But, as I said before that, we have some more quantum numbers, when you solve the Schrodinger equation for psi, these quantum numbers have to be defined.
但我说了，我们还有，其它的量子数，当你解，psi的薛定谔方程时，必须要，定义这些量子数。
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n l So negative e, which is sub n l, because it's a function of n and l in terms of quantum numbers.
也就是负的，E，下标是，因为它是一个,关于量子数，n，和，l，的函数。
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psi So we're going to for psi, and before that, we're going to figure out that instead of n just that one quantum number n, we're going to have a few other quantum numbers that fall out of solving the Schrodinger equation for what psi is.
我们要讲到，但在这之前，我们已经知道了,主量子数，现在我们需要知道，其他一些,解psi的薛定谔方程,所需要的量子数。
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So if, in fact, we want to describe a wave function, we know that we need to describe it in terms of all three quantum numbers, and also as a function of our three positional factors, which are r, the radius, phi plus the two angles, theta and phi.
实际上，我们想描述波函数，我们知道我们需要,用这三个量子数来描述它，同样，波函数还是,三个位置变量的函数，它们是r半径，还有两个角度theta和。
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