Friday, April 25, 2014

Science Friday: Planck's Quantum

Since I was in high school, I've wanted to understand quantum physics. In my first year at college, I felt called to ministry and so never continued that path. But in mid-life I've tried to get back into some of those old aspirations on the side.

One book I've had for years is George Gamow's, Thirty Years that Shook Physics (it has a Joseph Beth's bookmark in it from Asbury days). This past week I reread the section on Max Planck. Planck's reluctant proposal in 1900 launched modern physics. He didn't want to. He called his proposal "an act of desperation." He was not at all an "outside the box" type.

According to the story, Planck was working on what had come to be known as the "ultraviolet catastrophe" (I don't actually think that's quite right, but this is the best way to tell the story, it seems). If you have a bunch of gas molecules in a chamber, you expect over time that the energy of the molecules will eventually even out as the molecules bump into each other and share energy (the equipartition theorem). It's the same idea as what happens when you open the door between a hot room and a cold room. Eventually the temperature will even out.

(In reality, there is still somewhat of a variation, but most molecules statistically will have a certain average amount of energy at a particular temperature and those with more or less energy will be in decreasing numbers.)

Two scientists from the late 1800s (Rayleigh and Jeans) supposed that the distribution of energy in a "blackbody" (which absorbs all wavelengths of light)--or in a cavity made to mirror the effects of a blackbody--would also spread out similarly into waves of all the frequencies and wavelengths. Following the idea of equipartition, the total energy would begin to distribute itself into to each wavelength of light until every possible wavelength had roughly the same amount of the total energy.

Gamow has a helpful illustration. It would be like playing a note on the piano without a damper between the strings. In such a situation, the energy from playing one note would seep into all the other strings until each string in the piano corresponding to each key had 1/88th of the initial energy.

This isn't what happens, and it's a good thing too. What would happen if the energy of a fireplace soon spread into other wavelengths so that before long, the fireplace was spewing out ultraviolet and x-rays. Gamma rays would follow and you would soon die.

Planck's suggestion was that energy couldn't seep into higher frequencies of radiation as easily as into the lower frequencies. The higher the frequency, the higher the threshold of energy it took to distribute into that part of the spectrum. Light was not behaving like a continuous wave that spread out evenly to all frequencies but more like discrete packages of energy of differing sizes. The size of these packages was different at different frequencies.

I've tried to think of a good illustration, even to help myself understand exactly what Planck is suggesting. Consider this one a work in progress. Let's say there is an auditorium where the seats are arranged somewhat strangely. The front row has lots of cheap seats. The farther back in the auditorium you go, the seats are fewer in each row and they cost more.

So let's say you start off with a certain amount of energy in a blackbody, based on the temperature. It is like having a certain amount of money to spend on seats in the auditorium. The energy is distributed. Most of it goes to the lower frequencies because those seats are cheap. Yes, some of it goes toward the more expensive seats, but not nearly as much.

How much does a seat cost? Planck found he could make the graph in theory look like the real graph by introducing a number that would eventually be called Planck's constant (6.626 x 10-34 Joule-seconds, given the symbol h). A packet of energy at a particular frequency, E, was h times the frequency:

E = hf

That's how much a seat cost. A seat at a low frequency didn't cost that much. But the higher the frequency, the more expensive the seat.

Einstein would seal the deal on Planck's desperate theory five years later. Light was not a continuous wave. When you break things way down, you get to something like atoms of energy smaller than which you cannot go--photons.

Next Friday: Einstein and the photoelectric effect

1 comment:

Martin LaBar said...

Gamow was a good communicator, at least in his books.

He also had a sense of humor. He and a scientist named Alpher made a discovery, and when they published it, they added Hans Bethe's name as another author, without Bethe's knowledge. The reason, of course, was that they wanted it known as the Alpher, Bethe, Gamow paper.

See here: