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Atomic Structure
The Nature of ...
... Light and Quanta.
Light and Angry Bees

Light shows "particle-wave duality". Light travels in straight lines; it has a measurable velocity (about 300,000 kilometers/sec); when it crashes into something it's "momentum" is transferred to that object; it behaves as a wave; and has a series of different wavelengths and frequencies (color).

It was Isaac Newton, in 1666, who first determined the mixture of "colors" in white light, and explained many of the properties of light (such as it traveling in straight lines) as being consistent with light being a stream of tiny, tiny particles of almost no mass. These particles, or photons, cannot go around corners and are absorbed when they hit things (causing objects to be different colors). It all seemed to fit.

But the Dutch physicist Christiaan Huygens (1629-1695) had different ideas. He thought that light behaved as if it was a "wave". His evidence was thin, but he could explain why different beams of light can pass one another, cross paths, and generally mix without knocking each other around, by the fact that waves do this sort of thing all the time (think of how sounds echo around the room without mixing).

By the nineteenth century, the wave theory of light was starting to pick up stronger and stronger evidence. By carefully passing a single source of light through two slits, a pattern of dark and light bands were produced on a screen on the other side. These interference patterns could only be explained properly if light was behaving as a wave, and that waves when added together could either produce a band which was twice as bright (termed "in phase"), or which cancelled one another out and produced a dark band (termed "out of phase").

Particles cannot do this.

Careful measurement of the interference bands could be used to calculate the wavelengths of different types of light, and it was found that the kind of light we use to see things has wavelengths ranging from 760 nm (red) to 380 nm (violet), with a whole spectrum of wavelengths (and colors) in between.

At longer and shorter wavelengths there are other kinds of radiation; infrared, for example and ultra-violet. Along with light, these form a whole "spectrum" of electromagnetic radiation that we cannot detect with our eyes, but, never the less has a lot of interesting, different properties.

Like bees and electrons, light sometimes behaves as if it is a stream of particles, and yet has other properties that can only be explained if it is a wave.

Angry Bees
and Black Body Radiation

Shake a hive full of bees, and they will get upset. Within seconds clouds of angry bees will come streaming out of the hive and will spread out in all directions looking for the cause of their distress.

Warm a "perfect black body" (a theoretical object) and radiation will stream out from it like a swarm of angry bees.

In 1879, an Austrian physicist, Josef Stefan, showed that the total radiation emitted from such a body depended on only one thing - the temperature. The nature of the "black body" was unimportant, but if the absolute temperature was doubled (from, say, 300oK - room temperature - to 600oK - the temperature of melting lead) then the amount of radiation would increase by sixteen fold. This is now known as "Stefan's Law".

As well as the quantity of radiation increasing with temperature, the quality of that radiation changes as well. Stand next to a steam radiator at about 400oK in a dark room and you will feel the heat, but not be able to see anything. The radiation that is warming your body is in the infrared region of the spectrum of radiation, which cannot be seen by the human eye.

But stand in a dark room near a block of metal heated to 950oK and you will not only feel a lot more heat, you will also see the block of metal glowing a dull red color. Both the quantity and the quality (wavelength) of the radiation has changed and is now in the region detectable by our eyes.

Further increases in temperature cause the block to emit light in the orange and then the yellow range of wavelengths, and at 6000oK the filament in a light bulb sends off radiation in all the wavelengths of the visible spectrum. Which is why we use them to provide us with illumination!

It appears, therefore, that there is a steady increase in the number of angry bees leaving a hive, or amount of radiation leaving a black body, and a steady and gradual increase in the speed at which the angry bees are vibrating their wings, or the frequency/wavelength of the radiation as the temperature goes up and up.

At least so it appeared until someone started measuring what was actually happening.

Black-body Radiation

a black-body radiates energy through a small hole

this radiation passes through a grating, which sorts it out into a spectrum of different frequencies, which can be detected on a screen

the intensity of the radiation at all the frequencies are measured and recorded

the experiment is repeated at different temperatures

In 1893, the German physicist Wilhelm Wien used the closest thing to a perfect black body - a kind of furnace with a tiny hole in it's side - to study black-body radiation and the frequencies of the types of radiation being emitted from the tiny hole.

Sure enough, at a given and constant temperature (T), he could measure two things; the amount of radiation (the quantity, or intensity) and the frequencies of the radiation (the quality). At low frequencies the quantity, or intensity, of radiation was low, and as the frequency moved higher and higher values the quantity of radiation also increased. But at some point Wien found that as the frequency became higher, the amount of radiation (the quantity, or intensity) actually started to go down.

There was a peak value, a frequency at which the most radiation was taking place, at that given temperature.

When he repeated this experiment at a different, higher temperature (2T), he also got a peak value, and a new frequency at which most radiation was taking place. But the peak frequency was also higher, and as the temperature increased, so did the frequency at which the peak occurred. What was going on?

Since there are a lot more high frequencies than low frequencies a black-body should emit more and more radiation as the frequency increases. In theory, 16 times as much at the violet end of the spectrum than at the red end, and much, much more in the ultra-violet part of the spectrum. So much, in fact, that virtually all the radiation from Wien's experiment should have been ultra-violet (this is sometimes called the "violet catastrophe").

But this is NOT what Wien found, and nothing he, or others, could do would make the current theory fit the measured facts. A new idea or concept was needed, and this concept came from a German physicist called Max Karl Ernst Ludwig Plank.


Plank began be questioning the central assumption of black body radiation; that all frequencies were being radiated with equal probability. What if this "equal-probability" assumption was all wrong, as it certainly seemed to be from Wien's experiments?

So Plank proposed a different assumption; that the probability of radiation taking place from a black body actually decreased as the frequency of the radiation increased! This would account for the observed fact that there was a lot less radiation at the higher frequencies than the original assumption predicted.

However, at low frequencies the probability of radiation taking place was still quite high, and so the amount of radiation increased (as predicted) and as observed in Wien's experiment. But only up to a point (the peak of the graph), and then Plank's assumption took over and the amount of radiation that was observed went down as the frequency went up. So far it all fitted nicely, but why? What physical property could account for the Plank assumption?

This is where the "new" thinking came into the story.

How, or what, could account for the observed fact that the probability of radiation decreased as the frequency increased? Hummmmmm.....

Plank did not assume that radiation behaved like a hive of angry bees, but we can. Bees beat their wings at a given rate; they have a "frequency". They also come in different sizes; small bees, larger bees and big bees. The bigger the bee the faster they have to beat their wings to stay flying, so bigger bees have a higher "frequency". What if radiation behaved the same way?

Plank proposed that radiant energy coming from the Wien black box did not flow out in one smooth, continuous stream (like a blast of air, or water), but flowed out of the box more like bees, in discrete, lumpy quantities, which he called "atoms of energy".

A radiating black box gave off a stuttering discharge of "pellets of energy" the way a hive gives off a swarm of individual bees. Just as you cannot have "half a bee" or "one and a third bees", so you could not have "half a pellet of energy" or "two and a quarter pellets of energy". Energy, like bees, came in lumps.

Plank eventually called these "lumps of energy" quanta, from the Latin word meaning "how much" (since he did not know "how much" energy was in a quamtum).

Like different sized bees beating their wings at different frequencies, violet light radiation has twice the frequency of red light radiation, so the quantum of energy being radiated by violet light has to be twice the size of the quantum of energy being radiated by the red light.

The energy content (e) of a quantum of Plank's radiation is proportional to the frequency of the radiation (v). Big bees have to beat their wings faster, so have higher frequencies. Thus Plank could express the relationship between these two components using a simple formula, thus :-

e = hv

where h is a proportionality constant which we now name after it's discoverer, and call the Plank constant.

About the best value for Plank's constant is

0.0000000000000000000000000066256 erg-seconds

which is usually written 6.6256 x 10-27 erg-seconds.

So how big is a quantum of energy?

Orange light has a wavelength of about 600 nm, and a frequency of 5 x 1016 Hz (cycles per second). Multiply this value by that of the Plank constant and we discover that orange light is carrying quanta of energy in the range 3.3 x 10-10 ergs - a tiny, tiny value that is about a third of a billionth of an erg! (And ergs are not very large to begin with!). Quanta are not very big!

Albert Einstein took this type of thinking to it's logical conclusion. Light waves of different colors had different frequencies, wavelengths, and now - thanks to Plank - different "lumps of energy". Light, he said, should thus be considered particles or photons.

As with everything else in the universe, light had "particle-wave duality", and behaved as if it were "waves" under some circumstances, and as "particles (or photons) under other circumstances. This is one of the most difficult concepts for large objects, like us humans, to understand.

In our everyday lives objects have so much mass that their wave-like properties are undetectable, so we have no personal experience of particle-wave duality. But down at the level of photons, and electrons, the masses are so small that this duality is a fact of existence and must be at least appreciated (if not understood!) if a reasonable image of an atoms is to be presented.

"Lumpy energy" (quanta) and particle-wave-duality-properties must have their place when considering the behavior of electrons. Also, as they participate in the formation of atoms, electrons have to be seen with both these sets of properties at the same time. Not an easy task!

© 2003, Professor John Blamire