Chapter 33 Early Quantum Theory and Models of the atom 3.黑体辐射规律 1) Stefan- Boltzman equation斯特藩—玻尔兹曼定律 The rate at which an object emits energy via electromagnetic radiation depends on the objects surface area A and the temperature Tof that area in Kelvins and is given b M(r)=M,(T)dn=oT 0 This is called the stefan-Boltzman equation, and gis a universal (stefan-Boltzman constant 斯特藩玻尔兹曼常量 O=5.670×1038W.m2.K
Chapter 33 Early Quantum Theory and Models of the Atom １) Stefan-Boltzman equation斯特藩—玻尔兹曼定律 4 0 M(T) = M (T)d =T 8 2 4 5.670 10 W m K − − − = 斯特藩—玻尔兹曼常量 The rate at which an object emits energy via electromagnetic radiation depends on the object’s surface area A and the temperature T of that area in Kelvins and is given by This is called the Stefan-Boltzman equation, and is a universal (Stefan-Boltzman) constant 3. 黑体辐射规律
Chapter 33 Early Quantum Theory and Models of the atom 2)wien's维恩位移定律 Two important theoretical curves on blackbody based on classical ideas were those proposed by W. Wien(in 1896) 维恩位移定律 amT=b 峰值波长 常量b=2898×103m.K
Chapter 33 Early Quantum Theory and Models of the Atom Two important theoretical curves on blackbody based on classical ideas were those proposed by W.Wien (in 1896) . 2) Wien’s 维恩位移定律 维恩位移定律 m T = b 2.898 10 m K 3 = − 常量 b 峰值波长
Chapter 33 Early Quantum Theory and Models of the atom 例太阳的单色辐出度的峰值波长λ=483m 试由此估算太阳表面的温度 解由维恩位移定律 b2.898×103 T K≈6000K 483×10 m 对宇宙中其他发光星体的表面温度也可用这种方 法进行推测 Examples 33-1 and 33-2 on page 764
Chapter 33 Early Quantum Theory and Models of the Atom K 6000K 483 10 2.898 10 9 3 m = = − − b T 例 太阳的单色辐出度的峰值波长 ， 试由此估算太阳表面的温度. m = 483nm 解 由维恩位移定律 对宇宙中其他发光星体的表面温度也可用这种方 法进行推测. Examples 33-1 and 33-2 on page 764
Chapter 33 Early Quantum Theory and Models of the atom 3) Rayleigh- Jeans theory瑞利一金斯公式 M,(7)(10w(m2Hz) i瑞利一金斯公式 瑞利-金斯公式 654 实验曲线 M,T 2TV kT T=2000k 紫外灾难 v/10Hz
Chapter 33 Early Quantum Theory and Models of the Atom 3) Rayleigh-Jeans theory 瑞利—金斯公式 ( )(10 W/(m Hz)) 9 2 − M T 0 1 2 3 6 /10 Hz 14 1 2 3 4 5 瑞利 - 金斯公式 实验曲线 T = 2000k * * * * * * * * * * * * * * * * kT c M T 2 2 2π ( ) = 瑞利 - 金斯公式 紫外灾难
Chapter 33 Early Quantum Theory and Models of the atom Neither wiens nor rayleigh-Jeans formulations were in accord with experiment. Wien's was accurate at short wavelenths but deviated from exp. At longer ones, whereas the reverse was true for the rayleigh-Jeans theory. A cloud covered in fair skies of physics 物理学晴朗天空中的一朵乌云
Chapter 33 Early Quantum Theory and Models of the Atom Neither Wien’s nor Rayleigh-Jeans formulations were in accord with experiment. Wien’s was accurate at short wavelenths but deviated from exp. At longer ones, whereas the reverse was true for the Rayleigh-Jeans theory. A cloud covered in fair skies of physics ! 物理学晴朗天空中的一朵乌云!