Black body curve

[nickglyn]

Can someone pleas tell me why the curve of the black body peaks and then drops back down to zero when the wavelength reaches 0? I understand that the Rayleigh-Jeans curve violates the conservation of energy, so is that why there's a peak of intensity at a certain wavelength? Sorry for my incessant questions I just really need the help!

[Rikahs]

This is what i think and someone can correct me if im wrong but a black body completely absorbs and emits any EMR fired at it. However if i emit a ray of x frequency light at the black body, it doesn't mean its going to emit the exact the same frequency i shot at it. What it really does is emit an array of frequencies with varying intensities that all add up to the same amount of energy in the incidence ray. So the curve is essentially a graph that shows "how much of each frequency is emitted". Therefore the peak indicates the frequency of emr that was emitted the most (greatest intensity). Lets use a blue ball as an example. The blue ball emits many frequencies of emr however the highest intensity emr that it releases is emr of frequency corresponding to the colour blue  which is why we see it as blue. Therefore on its black body curve the blue colour frequency would be the peak of the graph.

Weird sort of explanation, but if it still doesn't make sense then just tell me.

[nickglyn]

Yeah man I get you. Just like when light hits a prism and is split into its coloured wavelengths. And I've finally understood now that the peaks of the graphs represent the greatest amount of quanta being emitted, which makes sense. Thanks for your help

[Cindy2k16]

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

[jamonwindeyer]

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!!

[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

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]

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!!

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]

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

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

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

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.

[jamonwindeyer]

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

Sure thing Cindy! So you said:

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. This peak is called the characteristic frequency/wavelength
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.

For this level of study, everything you've covered is excellent. You understand things really well! The bit in red at the end there is the only part that strikes me as slightly off. Remember, these energy changes can happen. There are "black bodies" (remember that a 100% true black body doesn't actually exist, but they get close) that have characteristic frequencies in the X-ray/UV/Gamma frequency ranges. It's low, but it happens. The important distinction here also is that we are talking about a perfect black body, which doesn't actually exist the radiation spectrum of a perfect black body covers ALL frequencies and wavelengths; it's just that the super high frequencies get next to nothing

[Cindy2k16]

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

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.

Sure thing Cindy! So you said:

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. This peak is called the characteristic frequency/wavelength
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.

For this level of study, everything you've covered is excellent. You understand things really well! The bit in red at the end there is the only part that strikes me as slightly off. Remember, these energy changes can happen. There are "black bodies" (remember that a 100% true black body doesn't actually exist, but they get close) that have characteristic frequencies in the X-ray/UV/Gamma frequency ranges. It's low, but it happens. The important distinction here also is that we are talking about a perfect black body, which doesn't actually exist the radiation spectrum of a perfect black body covers ALL frequencies and wavelengths; it's just that the super high frequencies get next to nothing

Thank you

[nickglyn]

Hey guys so I really appreciate all the feedback this discussion has provided, but I just need a tad more clarification with the curve.

The part of the curve where wavelength (the beginning of the curve) is very short means that EMR of high frequency is being emitted, but because of this high energy increase it means it is less likely for the body to emit a lot of quanta of energy (i.e intensity is low)? Is this correct?

And what exactly is the explanation for the decreasing intensity when wavelength increases? (sorry my teacher didn't exactly explain this very well!)

[jamonwindeyer]

Hey guys so I really appreciate all the feedback this discussion has provided, but I just need a tad more clarification with the curve.

The part of the curve where wavelength (the beginning of the curve) is very short means that EMR of high frequency is being emitted, but because of this high energy increase it means it is less likely for the body to emit a lot of quanta of energy (i.e intensity is low)? Is this correct?

Yes, that is correct

And what exactly is the explanation for the decreasing intensity when wavelength increases? (sorry my teacher didn't exactly explain this very well!)

Similar to the explanation for shorter wavelengths, purely in that quanta of those energy levels don't get emitted too much. This is because the energy differences between electrons are typically higher than those long wavelengths!

Just as an FYI to all while I remember; this is right on the edge of assessable content. Like, you are NOT going to be asked to explain the mechanics of the black body radiation curve. It's nice to understand, but not absolutely crucial.

[wyzard]

Hey guys so I really appreciate all the feedback this discussion has provided, but I just need a tad more clarification with the curve.

The part of the curve where wavelength (the beginning of the curve) is very short means that EMR of high frequency is being emitted, but because of this high energy increase it means it is less likely for the body to emit a lot of quanta of energy (i.e intensity is low)? Is this correct?

And what exactly is the explanation for the decreasing intensity when wavelength increases? (sorry my teacher didn't exactly explain this very well!)

You're right, at high frequency the blackbody has a lower tendency to absorb and emit energy due to the large energy differences, recall that the blackbody needs to absorb energy and make a jump of E = hf, so higher the frequency, the higher the jump which is more difficult.

As for low frequency/ high wavelengths, I've explained it in my previous post:

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.

In other words, it is more difficult to fit waves of long wavelengths in the box; think of trying to squeeze in long sticks into a small box, the longer the sticks, the harder it it.