radiation emitted by hot objects is called thermal radiation. recall that the total radiation power...
TRANSCRIPT
Radiation emitted by hot objects is called thermal radiation.Recall that the total radiation power emitted is proportional to T4, where T is the absolute Kelvin temperature.
Topic 7.1 ExtendedA – Quantization: Planck's Hypothesis
P = AeT4 FYI: Stefan's Power law
where = 5.6710-8 W/m2K4 Stefan-Boltzmann constant
and A is the surface area of the object. and e is the emissivity of the object and is a unitless number between 0 and 1 that depends on the material emitting the radiation.
Emissivity e
0 <-------------------------------------------------> 1
shiny <---------------------------------> dark
FYI: A good emitter = a good absorber.
mirror <-------------------------------------------------> blackbody
FYI: A "blackbody" is a perfect emitter (and absorber). IT IS AN IDEAL SYSTEM THAT ABSORBS AND EMITS ALL RADIATION THAT IS INCIDENT ON IT.
FYI: Since all bodies are above absolute zero, all bodies emit thermal radiation.
A small sphere covered with lamp black makes a pretty good blackbody and has an emissivity somewhat close to 1.An even better blackbody can be made by drilling a small hole in a hollow block. The hole itself acts as a blackbody.
Topic 7.1 ExtendedA – Quantization: Planck's Hypothesis
e = 0.5
tallow candle
e = 0.9
better blackbodyincident thermal radiation
FYI: A cavity blackbody, such as the one shown below, traps almost all the incident radiation, acting like a perfect absorber. Thus the hole acts like a nearly perfect absorber of radiation.
Thermal radiation comes in many visible colors - ranging from red to orange to yellow to white to blue - and each color represents a wavelength.Suppose we take our cavity blackbody and place a detector at the opening, and heat the cavity blackbody to successively higher temperatures, while measuring the frequencies of the emitted radiation. We get a family of graphs that looks like this:
Topic 7.1 ExtendedA – Quantization: Planck's Hypothesis
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Wavelength (nm)1000 2000 3000 4000 5000
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Two trends emerge:(1) The higher the temperature the greater the intensity at all wavelengths.(2) The higher temperature the smaller the wavelength of the maximum intensity.
FYI: Wien in fact came up with a mathematical relationship which describes point (2): namely maxT = 2.9010-3mK.
max is the wavelength at the maximum intensity.
maxT = 2.9010-3 mK Wien's displacement law
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Topic 7.1 ExtendedA – Quantization: Planck's Hypothesis
The sun releases its radiant energy into space through a 260-km-thick layer which we call the photosphere.The inner surface of the photosphere is at 6800 K while the outer surface is at 4500 K.What are the wavelengths of the maximum intensity radiation for the two surfaces?Use Wien's law: maxT = 2.9010-3mK. max=
2.9010-3 mKT
At 6800 K surface
max=2.9010-3 mK
6800 Kmax= 4.2610-7
m
max= 426 nm
At 4500 K surface
max=2.9010-3 mK
4500 Kmax= 6.4410-7
m
max= 644 nm
700 600 500 400Wavelength / nm
Visible Light
104 106 108 1010 1012 1014 1016 1018
Frequency f / Hz
Radio, TV Infrared Light X-Rays
FYI: By the way, remember the formula v = f we learned back in the wave section? The same formula works for light, where v = c, the speed of light. The speed of light is c = 3.00108 m/s.
The Electromagnetic Spectrum Microwaves Ultraviolet Light Gamma Rays
As far as classical wave theory goes, thermal radiation is caused by electric charge acceleration near the surface of an object.And accelerating electric charges produce electro-magnetic radiation.
Topic 7.1 ExtendedA – Quantization: Planck's Hypothesis
In a blackbody, classical theory (based on the number of standing wave modes) predicts that the intensity is proportional to 1/4.
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Wavelength (nm)1000 2000 3000 4000 5000
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The observed spectra look like these: The predicted spectra for the UV radiation looks like this: The predicted value of 1/4 fits the observations very well, as long as the wavelength is big enough.The predicted value of 1/4 fails miserably for short wavelengths.
FYI: Note that I as 0.
FYI: We call the failure of classical theory to predict blackbody radiation intensity at small wavelength the ULTRAVIOLET CATASTROPHE.
Topic 7.1 ExtendedA – Quantization: Planck's Hypothesis
In 1900, the UV catastrophe led German physicist Max Planck to reexamine blackbody radiation.
According to Planck's new theory, theoretical predictions could be made to work if energy were quantized.
THE PLANCK HYPOTHESIS
Classical theory allowed energy to take on any continuous value, but failed to predict intensities at short wavelength.
What this means is that the thermal oscillators that produce radiant energy can only produce "packets" of energy satisfying the formula
En = nhf, for n = 1,2,3,...
where h = 6.6310-34 Js
Planck's Hypothesis
Planck's Constant
FYI: Since Planck's Constant is so small, energy appears continuous under most circumstances. It is only when the wavelength becomes very small that the discontinuous nature of energy becomes apparent.
FYI: The smallest "chunk" of energy, called a quantum of energy, is given by E1 = hf.
Note that there is a different quantum of energy for each frequency.
Topic 7.1 ExtendedA – Quantization: Planck's Hypothesis
THE PLANCK HYPOTHESIS
What is the quantum of energy for violet light having a wavelength of 426 nm (from the inner layer of the sun's photosphere)?Recall that v = f, and that for radiant energy, v = c, the speed of light. Thus
c = f
f =c
so thatE = hf
E =hc
Quantum of Energy
E =(6.6310-34 Js)(3.00 108m/s)
42610-9 m
E = 4.67 10-19 J
FYI: According to Planck's hypothesis thermal oscillators can only absorb or emit this light in chunks which are whole-number multiples of the above energy.
FYI: Max Planck received the Nobel Prize in 1918 for his quantum hypothesis, which was used successfully to unravel other problems that could not be explained classically. The world could no longer be viewed as a continuous entity - rather, it was seen to be grainy.