How does quantum theory explain blackbody radiation? (1 Viewer)

[Giant Lobster]

The quantisation of light only explains the photoelectric effect. Theres no "threshold frequency" of light for heating things... is there? And so what if light can only be released in quantised amounts... i dont see the connection, and text books do a poor job of explaining "why" - they just say "what" and leave a gaping hole in the explanation.

What does quantum theory have to do with blackbodies in the first place?

As a side note, anyone know how quantum theory explains the ultraviolet catastrophe?

Thanks.

 

[t-i-m-m-y]

a brief but not complete explanation:

(actually this was for me the hardest part of physics)

u would have studied the wave-duality nature of energy (but probably not matter); enough to understand energy exists as discrete quantities

the threshold frequency only relates to the photoelectric effect- don't get them confused

my notes says:
A black body is a perfect absorber or emitter of radiation. The radiation emitted by a black body are
electromagnetic waves produced by vibrating charges. Calculations using classical theory physics
predicted that there would the radiance of shorter wavelengths would be a lot greater than those of longer
wavelengths. However, according to experimental results, the relationship between wavelength and
intensity followed a bell curve.
Planck developed a hypothesis that radiation emitted and absorbed by the black body is quantised. His
theory said that an oscillating charge can only have discrete values for frequency. The
temperature-wavelength relationship forms the basis of quantum theory. The small packets of energy
were called photons and contributes to the particle theory of light. When the frequency is limited to
discrete amount, it is referred to as being "quantised".
The photon model of light can be used to explain black body radiation, as radiation emitted is in the form
of discrete packets of energy to form a continuous wave.

^^^ i get all that i wrote in my notes maybe u dont

 

[wogboy]

text books do a poor job of explaining "why" - they just say "what" and leave a gaping hole in the explanation.

Perfectly describes the HSC physics syllabus, all you're required to do is pretend to understand the concept and hand wave the rest of the way to get a good mark, but it leaves a huge hole in your curiosity as to understanding the "why". Anyway enough of my ranting and back to the physics.

Black body radiation is the EMR (electromagentic radiation) emitted by a black body at a given temperature. You might ask why does a heated body emit EMR? It is because as the object is heated, the atoms & molecules oscillate, and as you know oscillating charges give rise to EM radiation. Now according to classical physics, these oscillations were taken to be like standing waves inside the black body (like when you pluck a guitar string, you form standing waves of many different frequencies at once depending on how long and stiff the guitar string is etc). If you remember back to Yr 11 physics, each different frequency of a single standing wave is called a mode. The criteria for a standing wave to contain a mode of wavelength L is L = 2x/n (for every positive integer n, and x is the length of the string). So you can see that as you reduce the wavelength, the number of modes grows hugely (the modes become very close together, when L is small).

Rayleigh and Jeans (the guys who studied black body radiation long before the quantum theory) assumed (wrongly) that each mode of oscillations was equally likely to occur at the same amplitude. And because as the wavelength is reduced, there becomes a huge number of nodes, and this meant that naturally, the black body must emit huge amounts of radiation at very short wavelengths (high frequencies). Although this theory was reasonably accurate for long wavelengths, this theory produced absolutely incorrect results for determining the intensity of the shorter wavelengths (if you heat a piece of metal a bit it doesn't start emitting huge amounts of gamma rays, otherwise you'd be dead!). Even more ridiculous, this theory predicted that as the wavelength approached infinity, the intensity of that wavelength did too, requiring infinite power! This is what the UV catastrophe was all about.

Later on, when Planck came along with his quantum theory, he proposed that not all of the modes have an equal probability occuring, and the modes with the lower frequencies (longer wavelengths) are significantly more probable. In the classical case of "continuous" radiation emission, all of the modes of energy would emit radiation together (more or less evenly). However because this is not the way it happens, but rather the radiation is emitted in "chunks", each chunk must only be produced by one mode. Seeing as the modes with the shorter wavelengths require more energy to emit a photon (E=hf), they are much less likely to emit a photon than the modes of longer wavelengths. On the other hand as mentioned before there are many more modes with short wavelengths than long wavelengths. The end result of this is that the intensity of the radiation emitted by a black body increases to a peak as you approach a certain frequency (as per the classical theory) but then it drops back down heading towards zero as you keep increasing the frequency beyond this point (as you can see from any black body radiation graph). This maths behind this is terribly complicated, so that's why I've avoided it.

Whew what a long post!

 

[t-i-m-m-y]

good stuff wogboy. i just read it and now it makes sense

now that we've done quantum mechanics@uni it all makes sense; how the probability of the modes are determined

 

[freaking_out]

in short: the blackbody radiation phenomena (along with others such as the photoelectric effect) led to the development of the quantum theory!

 

[Giant Lobster]

Originally posted by wogboy
Perfectly describes the HSC physics syllabus, all you're required to do is pretend to understand the concept and hand wave the rest of the way to get a good mark, but it leaves a huge hole in your curiosity as to understanding the "why". Anyway enough of my ranting and back to the physics...

...

Whew what a long post!

Wow thanks for the explanation, I think I understand the theory behind it... hmmm I can see why the HSC syllabus doesnt include even the theory because it took me several reads to comprehend

But then if that were the case they shouldn't have even mentioned quantum mechanics in high school physics

Thanks heaps

 

[freaking_out]

Originally posted by wogboy
Perfectly describes the HSC physics syllabus, all you're required to do is pretend to understand the concept and hand wave the rest of the way to get a good mark, but it leaves a huge hole in your curiosity as to understanding the "why". Anyway enough of my ranting and back to the physics.
...

yeah, they shouldn't call it physics anymore...and as i always say: that 4u maths has more fysics than hsc physics itself.

 

[Giant Lobster]

yeh i reckon

my friend looks at the mech chapter of 4u and asks if this is wot we do in physics... haha i wish!

id be so happy if physics purely newtonian mechanics and the QUANTITATIVE stuff about it, using real maths instead of pussy shit spoon-fed given equations.

 

[freaking_out]

Originally posted by Giant Lobster
yeh i reckon

my friend looks at the mech chapter of 4u and asks if this is wot we do in physics... haha i wish!

id be so happy if physics purely newtonian mechanics and the QUANTITATIVE stuff about it, using real maths instead of pussy shit spoon-fed given equations.

yeah i wish man...but then again hsc fysics is a bludge anyways.

 

[Xayma]

If you did that in physics, 90% of the people would drop it (which wouldnt be a bad thing, since the scaling would go up, except I probably wouldnt have been able to pick it up)

 

[Giant Lobster]

too much pussies doing physics anyway

 

[freaking_out]

Originally posted by Giant Lobster
too much pussies doing physics anyway

yeah, and worse still- more pussies are topping it too.

 

[Xayma]

Originally posted by Giant Lobster
too much pussies doing physics anyway

Yes but I need those pussies to make my rankings look good, and plus my school wouldnt of ran it with only 2 people doing it.

 

[Giant Lobster]

... good point

applying this logic, we need more pussies doing ext2 maths

wait, no theres plenty.

 

[freaking_out]

Originally posted by Giant Lobster
... good point

applying this logic, we need more pussies doing ext2 maths

wait, no theres plenty.

hehe yeah, a lot of kids doing 4u maths do it coz of peer pressure/ego....and hence u get ppl from my skool getting atrocious marks (i heard that one guy got 42 for his hsc mark).

 

[LiKe A FiSh]

i dont even do maths and i do well at physics, i was ranked 2nd... so im all for the spoon fed formulas, and plus we nomathers and 2uniters are kicking many of the 3uniters and 4uniters butts...because just because we dont do maths doesnt mean we couldnt, i chose to pick up Ext 2 English and drop maths which i was doing quite well at its quite illogical to presume that just because we dont do maths i wont get in the top bands for physics...and to presume that we doing physics will just improve your rankings because you can wipe the floor with us because i think you'll be in for a rude shock...plus you can be good at maths and not have a clue about science...or not be able to write what you understand

 

[freaking_out]

Originally posted by LiKe A FiSh
i dont even do maths and i do well at physics, i was ranked 2nd... so im all for the spoon fed formulas, and plus we nomathers and 2uniters are kicking many of the 3uniters and 4uniters butts...because just because we dont do maths doesnt mean we couldnt, i chose to pick up Ext 2 English and drop maths which i was doing quite well at its quite illogical to presume that just because we dont do maths i wont get in the top bands for physics...and to presume that we doing physics will just improve your rankings because you can wipe the floor with us because i think you'll be in for a rude shock...plus you can be good at maths and not have a clue about science...or not be able to write what you understand

yeah, i agree but all this ur saying is only applicable for "HSC Physics" not real physics (i.e u can't b bad at maths and b awesome at physics).

 

[Giant Lobster]

haha
in uni, physics is synonymous with applied maths. mr. english would be eaten alive without maths

hsc physics was designed to accomodate ppl like u who dont do any maths at all, in the spirit of being "fair" to everyone. I dont blame em. The result is that the course is... well, weird.

 

[freaking_out]

Originally posted by Giant Lobster
haha
in uni, physics is synonymous with applied maths. mr. english would be eaten alive without maths

hsc physics was designed to accomodate ppl like u who dont do any maths at all, in the spirit of being "fair" to everyone. I dont blame em. The result is that the course is... well, weird.

and hence the "mr. english" person tops it coz he can memorise better.