# Blockbody radiation question

1. Sep 8, 2006

### davepl

I have a (very basic) question on blackbody radiation (and no, its not my homework assignment... just trying to fill the gaps in some of the physics I missed 20 years ago when I -was- in school!).

As you heat an object, such as a block of metal, and as the temperature increases to higher energy levels, are light quanta emitted simultaneously at -all- the possible wavelength's predicted by Planck, or only at the shortest possible wavelength?

For example, if its "yellow hot", is it emitting red, orange, and yellow at the same time, or just yellow?

A second question, sort of tangential: why is there no "green hot"? The color spectra emitted after yellow seem to fill in all of the remaining color gaps, and go from yellow to white. I've read that the emissivity of metals makes it so they emit more easily in the blue wavelengths, but if that were the cause, I'd -expect- metal to look greensih when it was only "yellow hot". So you can see where I'm stuck :-)

Thanks!
Dave

Last edited: Sep 8, 2006
2. Sep 9, 2006

### lalbatros

First question

The black body spectrum is a contiuous spectrum: one may consider that -usually- each part of the spectrum contains some energy. By "usually" I mean:
- when considering high temperatures (say >= ambient)
- and wavelengths smaller than -say- centimeters​
This needs further explanations.
Let's forget a while about the hot piece of metal: it would require longer explanations to get at the same conclusion. Let's consider a large and empty oven maintained at a high temperature, well isolated, and let's assume its walls are perfectly reflecting.

In such a box the electromagnetic radiations must be "compatible with the conducting walls": the electric field must vanish along the walls (reflection).
Therefore the wavelength must be "an integer fraction of the size of the box" (L):

lambda = L/n​
Therefore the frequencies are integer multiples (n) of the smallest frequency: f

n = n fo with fo = c / L and c the speed of light.​
Conclusion: the spectrum is not really continuous, it is made of discrete frequencies fn , separated by a small frequency gap fo = c/L. For a dimension L=1m , the frequeny gap is fo = 300 MHz.
This is to be compared to some familiar frequencies (see wiki):
visible spectrum: 1 PHz = 1000000000 MHz
infrared spectrum: > 10 THz
microwaves: > 1 GHz = 1000 MHz​

Further conclusion: if you are looking at low frequencies (microwaves for example), you might discover that the spectrum is not really continuous. Of course: the only possible frequencies are the resonnance frequencies of the box. This is classical electromagnetism, well known in electronics, radrs, ...
On the contrary, in the visivble spectrum, it is practically a continuous spectrum, considering the high frequencies in th visible spectrum, as compared to the small gap (300 MHz for example).

There is more to be discussed on the role of quantum mechanics and photons in the BB radiation. This was discussed not long ago in this forum.

Second question
This should be looked in a bit more detail by really calculating the shape of the BB spectrum at different temperatures. But I think this will show the reason: when the metal heats up:
- not only does the main frequency of BB spectrum increase
- but the width of the spectrum increases also (proportional, I think)​
Therefore, the "green turn" cannot be seen because it is mixed up with many other colors.
In addition, it might be possible that the "green part of the spectrum" is rather small, which makes it even more difficult to observe.

I would be interrested to know how much % of the sun radiation lies in the visible spectrum. This can be calculated, but today I won't make calculations!

Michel

Last edited: Sep 9, 2006
3. Sep 9, 2006

### simic4

All frequencies o light are emitted at once with a certain distribution curve, the black body curve. taht is certain frequencies are favored over others. for example your yellow hot material will emitt quanta highly peaked around the yellow light frequency. The peak frequency, yellow inn the yellow hot material, is a function of temperature.

You can understand this by understanding what is temperature. the temperature of the material is just a measure of how much the atoms in the material (which forms the black body) are vibrating. a high temperature means they are vibrating alot. since the atoms in the material will vibrate with many different frequencies, they will all tend to emit quanta at different frequencies. however there will be a certain range of vibration in which most of the atoms fall, this is determined by the temperature. hence most of the atoms will be emitting quanta in a certain frequency range.

just to emphasize,, the fact that the material has a temperature, preassumes, the atoms are vibrating at many different frequencies, not at a single frequency. the state is just a bunch of random noise, the higher the randomness, the higher the temperature.

Last edited: Sep 9, 2006
4. Sep 9, 2006

### selfAdjoint

Staff Emeritus
All of the frequencies are generated, but the probability that a frequency will be generated is determined by the partition function, which depends on the temperature, leading to Wiern's law and the equilibrium frequency distribution.

5. Sep 9, 2006

### lalbatros

simic4,
davepl,

On wiki you can see the spectrum of an Incandescent flashlight.
It is very close to a BB spectrum at 4600 K.
The visible spectrum covers the small region of wavelengths between 400 nm and 700 nm.
You can see that the Incandescent flashlight spectrum is broader than the visible spectrum.
It also emits substancially in the infrared.
Clearly, the color emitted by a hot body is far from being monochromatic.
Its color is determined by the dominant part of the spectrum. But it contains a broad mix of other colors.

In colorimetry, there is a parameter called purity that measures how much a light is monochromatic. Monochromatic light has a purity of 100%, it corresponds for example to the light emitted by a laser or to a selected spectral line from a given atom. A light with purity=0% has a completely flat spectrum and corresponds to an inifinite temperature. When considering human vision (400nm-700nm) there is very little difference between sunlight (6000°C) and a flat spectrum. Therefore, on the colorimetric diagram, sunlight has a very small purity (nearly 0, close to the infinite temperature).

The chormaticity diagram is explained on a nice pdf paper by G Hoffmann.. In page 10 of this document you will see the position of blackbodies colors for different temperature. You will see that when the temperature increases, the color point moves to the center of the diagram. This means that the purity decreases when the temperature increases. This means also that the spectrum broadens. However, at lower temperatures (red) the spectrum is not really pure, but its purity is much higher.

I hope you enjoy coloritmetry and BB!
Quite an interresting subject because it mixes physics and eye physiology.

Michel

Last edited: Sep 9, 2006
6. Sep 9, 2006

### Staff: Mentor

Black body radiation concepts -

http://hyperphysics.phy-astr.gsu.edu/hbase/bbcon.html

http://hyperphysics.phy-astr.gsu.edu/hbase/mod6.html

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