Low Frequency Radiation

低频辐射

The classical and quantum expressions for radiation from a hot object are

Making use of the series expansion of the exponential:

利用指数函数的级数展开：

Comparison plot

对比图

热物体辐射的经典和量子表达式

Index

Blackbody radiation concepts

索引黑体辐射概念

HyperPhysics***** Quantum Physics

HyperPhysics ***** 量子物理

R Nave

Go Back

Probability for Higher Energy

高能的概率

Why does the Planck radiation curve fall below the classical Rayleigh-Jeans Law? The origin of the drop involves the probability of higher frequency (higher energy) modes being occupied. It may be helpful to compare to the probability for higher energies in an ideal gas as given by the Maxwell distribution. Given an energy on the order of the thermal energy, what is the probability that the system could be found at multiples of that energy?

The classical view treats all electromagnetic modes of the cavity as equally likely because you can add an infinitesmal amount of energy to any mode. The quantum view expressed in the Planck hypothesis is that you either add the energy of a whole photon, or you don't add any at all. Since the excitation of a high frequency photon takes an energy high above the average thermal energy, it is therefore less likely. Thus the radiation curve falls progressively further below the classical expectation.

为什么普朗克辐射曲线低于经典瑞利-金斯定律？这种下降的原因涉及高频率（高能量）模式被占据的概率。可以将这种现象与理想气体中高能量状态的概率进行比较，如马克斯韦分布所给出的。给定的能量大约等于热能，系统处于该能量的倍数状态的概率是多少？经典观点认为，腔体中的所有电磁模式都是等概率的，因为你可以向任何模式添加无限小的能量。而量子观点则如普朗克假设所表达的，你要么向系统添加一个完整的光子能量，要么根本不添加任何能量。由于高频率光子的激发需要的能量远高于平均热能，因此这种可能性更小。因此，辐射曲线逐渐低于经典预期。

Index

Blackbody radiation concepts

索引黑体辐射概念

HyperPhysics***** Quantum Physics

HyperPhysics ***** 量子物理

R Nave

Go Back