Main Sequence Page 4

The Photoelectric Effect and the Nature of Light
This page includes a reasonably complete (but not exhaustive!) How-to Experiment on the photoelectric effect.
It also includes a How-to Experiment showing that light behaves like very small rocks.
It also includes a How-to experiment that proves once and for all that light behaves like ripples on the surface of the ocean.
Yet another How-to will demonstrate light as a form of energy.

Contents
Introduction
Demonstration Procedure
Experiment Ideas
Experimental Results
Why It Shouldn't Work
Planck's 1900 Blackbody Law Derivation
Einstein's 1905 Blackbody Law Derivation
Einstein's Addenda
Einstein's 1909 Continuation of the Thought
Concluding Remarks

Introduction: Some Historical Notes
In 1905, to cut a long story short, when we were five years into the quantum age, Albert Einstein took physics an important step further by finding a new way of deriving an already-existing formula. Which is kind of amusing if you think of progress as 'new results' and not 'new ways of arriving at old results.' Five years before, late in 1900, Max Planck had published the correct expression for blackbody radiation as a function of temperature and frequency using an hypothesis of oscillators constrained to vibrate at quantized energies. If this makes no sense to you, join the club. It makes no sense to me either. But taking that in stride I'll discuss further the events of 1905, a very famous year in physics, which is entirely the fault of Professor Einstein.

The 1905 Einstein derivation of Planck's blackbody radiation law followed an alternative path, but the crucial thing was that this alternative path relied upon new physical ideas. (Incidentally here is a 'modern derivation' of this result.) Consequently physics was drawn closer to an inevitable massive revision of its most fundamental laws concerning the behavior of matter on microscopic scales. After giving this new derivation of the blackbody formula, Einstein proceeded to use his new ideas to provide explanations for several hitherto-puzzling phenomena, the most famous being the photoelectric effect. This I will describe briefly below.

The 1905 paper was a landmark in the historical period from 1900 to 1925 in which the groundwork was established for the correct theory of quantum mechanics. During this same period, particularly from 1904 through 1917, Einstein was working on relativity theory which also concerns matter and energy (among other things like space and time and gravity!) In due course the two theories--quantum mechanics and relativity--began to overlap, or to put it another way, they had to be reconciled with one another. After all, if both theories were correct then they had to be mutually consistent. And according to experiment they both seemed to be correct.  (This reconciliation process is very interesting and it is still in progress today.)

Photoelectric Effect explained by analogy, and why analogies are the fool's gold of quantum mechanics

The PE-effect is the liberation of electrons from a material due to bombardment of that material by light.

If an electron in a piece of zinc is available to conduct electricity then it is easily pushed about by electric fields. I don't know if this is a good analogy but if you consider a pond in the winter which has frozen over, there might be some bushes along the banks that are frozen in place, poking up through the ice.  There might be some people skating around on the clear ice at the center of the pond as well. The bushes are not really available for motion-based activities but the skaters are. In fact you might start pushing your friend around on the ice in any direction you like, provided you can get a little traction, just for your amusement. If your friend is amused by this sort of thing as well, you might even give him a hard enough shove at the margin that he is knocked off the pond altogether.

There are two remarks I'd like to make about this analogy before getting down to the experiment. First: In this analogy your friend is an electron, the frozen pond is the piece of zinc, and you are a photon. (The bushes are more electrons that are stuck in the pond.) You are exerting an influence on him by transferring energy, perhaps enough energy to knock him out of the pond. That is, light can transfer energy to electrons and this analogy is a version of Einstein's explanation of the photoelectric effect: photons can knock electrons loose from zinc or other materials. This was a profound step in trying to understand light, since it had been earlier well established that light was more analogous to ripples on an un-frozen pond, and not analogous to a guy shoving skaters around on ice.

The second remark concerns the nature of these analogies. Feynman said many times (to paraphrase a bit) that light and electrons are not like ripples on ponds and they are not like people throwing each other off of frozen ponds and they are not like baseballs and they are not like bushes and they are not like anything else we know about. So these analogies always suffer from being incomplete, almost wishful thinking. The problem is that analogies provide a false sense of security. Picture Wile E. Coyote traversing a gorge by nailing boards together end-to-end. It only works part way across.

Analogies about how to learn are somewhat safer, because who cares how I learn it eventually anyway? To employ one: The path to the top of the mountain of "understanding the nature of light" is a bit like the path out of Alice's looking-glass garden: I'm obliged to start off in apparently the wrong direction and traverse a long and strange pathway to reach the top. Once there I can think in the wrong way, necessary to properly understand how light works (and how electrons work (so I'm told)) independent of analogies with things I are familiar with. I am not there yet, not there yet. But this doesn't prevent me from shining violet light on pieces of zinc.

Demonstration Procedure
Per habit I've tried to break this into a series of reasonable steps. The idea behind this demonstration is that we have an effect-amplifier that reveals the motions of billions of electrons. That is a little strip of foil that hangs down against a backing plate (or flush with a second piece of foil). The foil is suspended from above, as a hinge, so that if excess charge is distributed throughout the metal the foil wil respond by hinging upward. That is, the electrons will repel one another and this is apparent in the motion of the foil.

All this would indicate that the electrons would really like to fly away from the crowd of other electrons. Alas they can not, and we are told this is due to a little energy barrier or 'work function' endemic to the metal conductor. This barrier must be overcome for an electron to escape. Enter the photons. Each photon-electron interaction is a transfer of energy, in fact precisely the energy of the photon. We choose a metal (zinc) with a work function about equal to the energy of a violet photon and now the stage is set for electron liberation by light bombardment. Of course once an electron is liberated it will be pushed away by the others thereby depleting the electroscope of charge. In consequence the foil will gradually relax back to its uncharged position.

Step 1: Obtain some light sources. One of them must be a black light or other source of violet/ultraviolet light. I use an old EPROM eraser with the cover snapped off. I also have a Helium Neon laser which is red light and of course incandescent and fluorescent lights are easy to come by. Below is a photo of the key item, the EPROM eraser. An EPROM is a type of microchip, an Erasable Programmable Read-Only Memory chip is what it stands for I think. These have little windows one can illuminate with UV to erase the chip's  contents so that it may be reprogrammed.

UV source

Below I'm using a sharp pointy little tool to push a switch that turns on the UV bulb. You can see that plenty of blue light comes out as well. This can be held near the zinc to bombard it with UV photons. Don't look at this picture! UV light is bad for our eyes.

UV source lit

Step 2: Obtain or build an electroscope. If you decide to build one there are lots of designs and examples on the web. They often involve suspending a folded piece of foil from a little metal hangar inside an Erlenmeyer flask. (My friend Bill points out that black rubber stoppers can be conductive so try and stick to cork.) I went ahead and ponied up $30 for this gold-leaf electroscope.

escope no charge

The photo above is a little "busy" but hopefully the basic idea is apparent: A sealed chamber with a glass front panel and a metal rod poking through the top, details to follow. But why, for example, are there apparently razor blades taped to the front glass? What is the point of the comb? What's up with the nail taped to the top post? Here are the answers:

escope charged

And just to make sure it is clear that the gold foil is really suspended away from the backing plate, here is a zoom-in photo.

escope charged detail

The nail is galvanized which means that it is coated with zinc. Zinc has a very small work function as metals go, only about 3.08 electron volts. Violet photons carry about this much energy and ultra-violet photons carry more according to the formula

E = h x nu = h x c / lambda.

E is energy, h is Planck's constant (without the two x pi; this is h and not h-bar), and nu is the frequency of the light. c is the speed of light, about 3 x 108 cm / sec and lambda is the photon wavelength. Visible light ranges from 400 -- 700 nanometers (nm). My personal way to remember how to calculate energies easily is: A 100 nm photon has energy 12.4 eV. A 200 nm photon has energy 12.4 / 2 eV, a 300 nm photon has energy 12.4 / 3 eV and so on.

Step 3. Obtain a galvanized nail and tape it to the electroscope post. As described above this is entirely because the galvanization is link and we should be able to knock electrons out of zinc with very-violet photons.

Step 4. Obtain a bit of sandpaper and lightly sand the nail. This removes any surface oxidation, exposing unoxidized zinc. The clean zinc should work great for at least a couple of hours.

Step 5. Find a comb and find somebody with dry hair. Steal some electrons from your volunteer and charge the electroscope. That is, run the comb through somebody's hair and then touch it to the nail. The electrscope leaves should fly apart, demonstrating that you have either added or removed some charge. We suppose this adds negative charge but proving this is another matter.

Step 6. Illuminate the zinc (the nail) with UV light. The electroscope leaves should collapse.

Experiment Ideas
This demonstration is not very astounding... in fact it's rather dull at first blush. Getting something out of this is more a gradual process of experimenting until it's apparent that something a little odd is going on. It is an excellent opportunity for inquiry, particularly if we add a few more tools, which this section describes. The full impact of the photoelectric effect however is really apparent in the context of pre-1905 ideas about light.

Try shining other light sources on the nail.
Try shining light on other parts of the electroscope (on the foil, particularly).
Try hitting the nail with laser light for a long period.
Try putting positive charge on the electroscope (silk/glass rod).
Limit the area of exposure by covering the nail except for the head.


Experimental Results
I set up a solar cell circuit to measure the power of applied light sources.

Why This Demonstration or Experiment Should Not Work
Discuss the energy inherent in the laser beam versus that of the UV bulb. Include calculations of numbers of photons in both cases. Assume some awful efficiency for the solar panel.

Planck's Derivation of the Blackbody Radiation Law
Sketch this will remarks on harmonic oscillators.

Einstein's Derivation of the Blackbody Radiation Law
The text should be entirely about the physical ideas for this versus the previous sections. Here is a modern approach to deriving the PRL.

Einstein's Addenda to this Derivation
How PE-effect and the other 2 or 3 things were accounted for.

Einstein's 1909 Continuation of the Thought
The point of the 1909 paper in taking another step towards the identity of light that served.

Concluding Remarks... where next?
Concerns statistics and the relationship between microscopia and bulk material properties, another version of our signal amplifier mentioned in the phenomena page. A box of gas is itself an experimental device, a kind of cascade amplifier...

Might also mention in here that temperature is very important to descriptions of gas, defer more on this to another page.

From here segue into a discussion of non-causal physics in the 20th century and the introduction of probability. I'm very interested in the open-endedness of Einstein's work showing photons are quantized when appropriate and the hint this gives about uncertainty, the loss of predictive causality. This is a huge conceptual leap on a par with the preliminary suggestion that light is quantized. So Einstein took a pretty good run at the edge of the pond but stopped at the last second, and the irony that he shoved a lot of other physicists off the pond regardless of his own reticence. The reticence would have been lost but for the magnitude of everything he accomplished.

Outline the very important question (from my list) of how a timescale is determined for a given probabilistic problem. For example radioactive decay, or stellar nucleosynthesis (hydrogen chain, carbon cycle).

Finally I've found a simple problem in discrete probability that is a good way of getting immersed in probability and counting possibilities (combinatorics). The problem is this: Suppose you have a handful of dice and you throw them all at once. You examine the dice and remove any which came up "6". Then you scoop up the remaining dice and throw them a second time. Again you scoop out the "sixes" and repeat. If you are talented, you will quickly reduce your original pile of dice to nothing. If you are not so talented (or fortunate) it will require many throws to eliminate all the dice.  But...

...how many throws should it take on average?

Previous
Next
Home