Ultraviolet Catastrophe


black ball

A blackbody absorbs and emits radiation equally well, but does not reflect

The "black" means it does not reflect.

glowing ball

But it can glow ... a lot! 

Because it emits radiation really well.


The Sun is an almost perfect blackbody. 

glowing metal rod

But let's use a metal rod in our examples. 

What happens when we heat the rod? 

It absorbs the energy and gets hotter.

white hot metal

It emits radiation and we see it glow.

First a dull red, then brighter and brighter until it gets white hot.

Why the color change?

It is because the glow covers more and more of the lower wavelengths. 

In the graph below we see how much radiation is given off at three different temperatures.  First let's look at the "actual" curves:

blackbody graph


The Sun's external region averages 5780 K, so it looks white when viewed in space (but can be yellow to red when viewed through our atmosphere).

Interesting that our eyes see radiation in that exact range!


Shorter wavelengths have higher frequency and higher energy:


Energy is directly related to frequency:

E = hf

  • E is energy
  • h is "Planck Constant" equal to 6.62607015×10−34 J/Hz
  • f is frequency

Higher frequency has higher energy.

With that fact, and with the blackbody free to radiate in all wavelengths, we should get the "Theory" curve (graph scale is now different):

blackbody theoretical

There should be a huge amount of ultraviolet. We could not exist in such a universe.

Thankfully we get the "Actual" curve instead, with only a little ultraviolet! But Why?

This baffled people for years and was called the ultraviolet catastrophe.

But then a guy call Max Planck came up with an idea that Einstein developed into a solution to it all.

It is because energy comes in little packets, called "quanta".

Higher frequency quanta have more energy, right?

But it is more likely for the energy to be emitted as many low energy quanta (such as infrared) than a single high energy quantum (such as UV). 

So we get something like this (illustration only):

blackbody emission
Here we have just one UV quantum,
some visible light quanta, and lots of IR quanta.
cleaning fluid and washcloth

Like keeping your house clean: many small cleans, a few medium cleans and sometimes a really big clean.

Thus high energy levels such as ultraviolet are simply more rare.

Problem solved!

And a whole new field of study was created: Quantum Physics!