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Black body curve

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nickglyn:
Yeah I get what you're saying. Sort of how in chemistry with AES, the energy emitted from the drop of an excited electron down to its ground state corresponds to the amount of input energy required to put it there. Makes sense!

My teacher never went through the "probable" outcome of an energy jump, nor the "UV Catastrophe"...had to learn it myself haha

nickglyn:
Thanks everyone!

wyzard:
Ah blackbody radiation 8)

The reason for the shape of the black-body curve, where it dies out at high and low frequency, leaving a peak in the middle, is due to two separate things. I'll explain each one.

In a blackbody containing EM waves, the waves in the blackbody is modelled as standing waves in a box. At higher frequency, EM waves have lower wavelength, so more waves can be squeezed into the box. Classically, there is no limit on how much EM wave can fit into the box, as the energy carried by them does not depend on their frequency/wavelength, which led to the Ultraviolet Catastrophe where the intensity blows to infinity as frequency goes up, predicted by Rayleight-Jeans. On the other hand, for EM waves with low frequency and high wavelength, fewer can be fitted into the box, hence the blackbody curve dies down to zero when frequency goes to zero.

To resolve the Ultraviolet Catastrophe, Planck has to introduce the notion that for each frequency of light, atoms can only absorb and emit discrete amount of energy given by the formula E = hf, which is now known as the energy of the photon. Meaning that at high frequency, the atom either have a absorb a high amount of energy, or don't absorb it at all, there is no in between. And the larger the jump in energy, the less likelihood the atom will absorb the energy.

Hence at higher energy levels, even though more wave can be squeezed into the box, the atoms in the blackbody is deterred to make such a jump to such high amount of energy needed. This suppresses the infinite growth in intensity and presses down to zero at high frequency.

Cindy2k16:

--- Quote from: jamonwindeyer on October 24, 2016, 10:58:05 pm ---Just want to accentuate some things in the awesome discussion above:

1- The peak of the black body curve corresponds to the frequency where the most quanta are emitted. That was explained really well above so awesome!
2- The position of that peak is dependent ONLY on the temperature of the black body. That's Planck's Law; what the body is made of and all other factors are irrelevant. Temperature alone determines it! :)

Thanks to everyone above who lent a hand!! ;D

--- End quote ---

Hi Jamon thanks for ur addition to the post! could u just clarify if my understanding of blackbody radiation was okay? I've never really had it checked with other people and sometimes I do learn incorrect things at school (my physics teacher isnt....the greatest)
Thanks :)

wyzard:

--- Quote from: Cindy2k16 on October 24, 2016, 10:11:55 pm ---Hi the way my teacher taught me, is that when an atom (of the blackbody) absorbs a packet of EM radiation , it undergoes a change in energy and an electron jumps to a higher energy level using the energy absorbed. However because electrons are unstable in this state, they soon return to their original energy level. When they return to their energy level, they emit a packet (quanta) of radiation. The greater the energy gap (from the energy level they hopped up to and the original) the more energy is in the emitted packet of light. (and the higher the energy, the smaller the wavelength)
Some energy jumps are more probable than others at given temperatures, resulting in the peak wavelengths.
In order to emit short wavelength radiation such as UV, X-ray or gamma rays, atoms need to undergo a very large change in energy that corresponds to the energy of UV/gamma/Xrays. But such large energy ranges dont exist in atoms so it's not possible. Thus blackbodies cannot emit such short wavelength/high energy radiation.

But I don't think the syllabus requires you to really explain to this depth and rather you just need to know to say that Planck's proposal that black body radiation was quantised solved the UV catastrophe and explained the black body radiation curve

--- End quote ---


--- Quote from: Cindy2k16 on October 24, 2016, 11:53:38 pm ---Hi Jamon thanks for ur addition to the post! could u just clarify if my understanding of blackbody radiation was okay? I've never really had it checked with other people and sometimes I do learn incorrect things at school (my physics teacher isnt....the greatest)
Thanks :)

--- End quote ---

You've got the main idea right, once atoms absorbs energy it will become unstable and emit it out again. ;D

The bit where you're a little off is saying that large energy difference don't exist in atoms so it does not absorb or emit high frequency EM waves, such as UV, X-ray and gamma rays. The reason why the it doesn't absorb and emit light at high frequencies is more subtle and has actually nothing to do with energy levels. The blackbody has all energy levels available to them. (Recall the band-gap energy for solids)

The reason actually comes from statistical physics, where it states that if the energy difference between states is higher, the lower the probability of such a transition will happen. In other words, the larger the energy gap, the harder it is for the atom to jump up, so they are deterred to absorb high energy photons with high frequency. In fact if you look closely, the blackbody does emit at high frequency, its just that the intensity is very very tiny so we don't really observe it in practice.

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