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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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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 the relationship that he put forth is that the momentum is equal to Planck's constant times nu divided by the speed of light, or it's often more useful for us to think about it in terms of wavelength.
爱因斯坦提出的关系式是,动量等于普朗克常数,乘以υ除以光速，或者用波长来表示,通常更容易让我们想明白。
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It is the ratio of the Planck constant to its momentum .
那就是普朗克常量,比上它的动量。
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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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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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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。
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And finally we have Planck's constant here, which we're all familiar with.
最后这个是我们，都很熟悉的普朗克常数。
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There is the Planck Constant, number five.
有普朗克常数在第5个。
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What Einstein then clarified for us was that we could also be talking about energies, and he described the relationship between frequency and energy that they're proportional, if you want to know the energy, you just multiply the frequency by Planck's constant.
爱因斯坦阐述的是我们,也可以从能量的角度来谈论，他描述频率和能量之间的关系,是成比例的，如果希望知道能量值，你用普朗克常数乘以频率就可以了。
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So, if we start instead with talking about the energy levels, we can relate these to frequency, because we already said that frequency is related to, or it's equal to the initial energy level here minus the final energy level there over Planck's constant to get us to frequency.
如果我们从讨论能级开始，我们可以联系到频率上,因为我们说过频率和能量相关,或者说等于初始能量,减去末态能量除以普朗克常数。
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So, we can get from these energy differences to frequency h by frequency is equal to r sub h over Planck's constant 1 times 1 over n final squared minus 1 over n initial squared.
所以我们通过不同能量,得到不同频率，频率等于R下标,除以普朗克常数乘以1除以n末的平方减去。
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And I use the term photon here, and that's because he also concluded that light must be made up of these energy packets, and each packet has that h, that Planck's constant's worth of energy in it, so that's why you have to multiply Planck's constant times the frequency.
我这里用光子这个词,是因为他还总结出光,必须由这些能量包组成，每个能量,包有这个h，普朗克常数代表,里面的能量，所以这就是为什么你们,要用普朗克常数乘以频率。
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