You see, the quantum condition, by putting quantization into the moangular mentum it is propagated through the entire system. Orbit dimensions are quantized.

你们看，量子条件，通过把,角动量量子化，它就能在这个系统中进行传播,同时轨道大小也被量子化。

麻省理工公开课 - 固态化学导论课程节选

All right. So let's look at some of these wave functions and make sure that we know how to name all of them in terms of orbitals and not just in terms of their numbers.

好，让我们来看一下,这些波函数,并确定我们都知道,怎么用轨道,而不仅是量子数来命名它们,一旦我们可以命名它们。

麻省理工公开课 - 化学原理课程节选

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。

麻省理工公开课 - 固态化学导论课程节选

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？

麻省理工公开课 - 化学原理课程节选

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。

麻省理工公开课 - 化学原理课程节选

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。

麻省理工公开课 - 化学原理课程节选

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。

麻省理工公开课 - 化学原理课程节选

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？

麻省理工公开课 - 化学原理课程节选

So, what he did was kind of impose a quantum mechanical model, not a full one, just the idea that those energy levels were quantized on to the classical picture of an atom that has a discreet orbit.

还不是完整的,只是这些能级，是量子化的概念，作用到原子有分立轨道的经典原子模型上,当他做了一些计算后,他得到有个半径,他算出来。

麻省理工公开课 - 化学原理课程节选

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。

麻省理工公开课 - 化学原理课程节选

So, molecular orbital theory, on the other hand, is based on quantum mechanics.

另一方面分子轨道理论，是基于量子力学的。

麻省理工公开课 - 化学原理课程节选

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。

麻省理工公开课 - 化学原理课程节选

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。

麻省理工公开课 - 化学原理课程节选

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。

麻省理工公开课 - 化学原理课程节选

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。

麻省理工公开课 - 化学原理课程节选

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？

麻省理工公开课 - 化学原理课程节选

And that's just to take 1 the principle quantum number l and subtract it by 1, and then also subtract from that your l quantum number.

主量子数,减去,再减去，量子数,你们可以对1s轨道来验证一下。

麻省理工公开课 - 化学原理课程节选

l So, if we're talking about a 4 p orbital, and our equation is n minus 1 minus l, the principle quantum number is 1 4, 1 is 1 -- what is l for a p orbital?

我们方程是n减去1减去，主量子数是，4，1是1，--p轨道的l是多少？,学生：

麻省理工公开课 - 化学原理课程节选

For an f orbital, what is the quantum number l equal to?

对于一个，f，轨道，它的角量子数，l，等于几？

麻省理工公开课 - 化学原理课程节选

And we can generalize to figure out, based on any principle quantum number n, how many orbitals we have of the same energy, n and what we can say is that for any shell n, there are n squared degenerate orbitals.

我们可以总结出来，在，主量子数为n的情况下，同一个能量上，有多少个轨道，我们可以说，对任何壳层，有n平方个简并轨道。

麻省理工公开课 - 化学原理课程节选

n So the velocity is given by this product of the quantum number n Planck constant 2 pi mass of the electron time the radius of the orbit, which itself is a function of n.

速度是量子数,普朗克常数2π乘以轨道半径的值,它自身也是n的函数。

麻省理工公开课 - 固态化学导论课程节选