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The Photoelectric Effect

Background

In 1887, the German physicist Heinrich Rudolf Hertz discovered an interesting property of matter. This property is that physical materials emit charged particles when they absorb radiant energy (eg, light). Of course, not all substances absorb radiant energy, and the ones that don't will not emit charged particles. But it could readily be established that some substances do behave this way.

Hertz initially observed that the minimum voltage required to draw sparks from a pair of metallic electrodes was reduced when they were bathed in ultaviolet (UV) light, such as from a mercury vapor lamp. The more intense the UV light, the lower the required voltage became.

In the broadest sense, the substance in question can be solid, liquid, or gaseous; the radiant energy must be visible light, UV; X-rays; or gamma rays (cosmic radiation). The charged particles can be electrons or ions. However, in general practical use, the substance is a metal plate and the charged particles are electrons.

In any case, a second German physicist, Philipp Lenard, studied this phenomenon using a metal plate, and in 1900 concluded that the charged particles emitted were the same as those found in cathode rays. That is, they were electrons. By 1902, it had been shown that the resulting current (called photoelectric current because it was caused by light) is proportional to the intensity of the light causing it for any given frequency of light energy, and that the maximum kinetic energy imparted to any electron is independent of the intensity of the light, but is directly proportional to the frequency of the light.

In 1905, Albert Einstein worked out the primary equation involved, and by 1912, the requisite measurements could be made with high precision. These experiments confirmed the conclusion that light is not a continuously wave-like phenomenon, but rather involves particle-like "corpuscles" of energy, now called photons, which are the quanta of electromagnetic energy.



The Experiment

The experiment itself is now performed in appropriate physics classes at most colleges and universities, and possibly in some high schools. It isn't difficult to perform, and if proper care is used, will give quite accurate results.

The classic photoelectric experiment

We begin with a photoelectric tube (or phototube), which is a vacuum tube containing a metal plate curved into a half-cylinder (the anode) and a thin wire electrode (the cathode) along the axis of the cylinder. The figure to the right shows this as seen from the top. We use a very sensitive meter, called a galvenometer (G), to measure the current passing through the tube, and a variable voltage source (V) to control the voltage applied between the two electrodes inside the tube. Finally, we add a light source (usually a mercury vapor lamp, but it can be an arc light or even a tungsten filament light bulb), and a colored filter to limit the light striking the photoelectric tube to a single frequency.

With no light, of course, the current through the tube will be zero, regardless of the applied voltage. (Yes, there is a slight capacitance between the metal plate and the wire, and a high enough voltage will cause an arc. But the capacitance is very slight and will charge quickly, and we won't be using anywhere near enough voltage to cause any problems.) So we turn on the light, place one of our colored filters between the light and the phototube, and begin our measurements.

The first thing we note is that if we reverse the polarity of the voltage source V, increasing the voltage or the intensity of the light will increase the current flow. This seems logical; the light is "kicking" electrons off the metal plate, and they are attracted to the now positively-charged wire electrode. The more light, the more electrons and hence the higher the current.

However, when we make the wire electrode negative with respect to the metal plate as shown in this figure, we begin to observe some interesting effects. First, red light, infrared (IR) radiation and anything of a lower frequency will not excite the phototube enough to enable current to flow. You pretty much have to get up at least to green light before you can measure a reaction. (This may vary depending on the specific metal coating the surface of the curved electrode.)

Once you find a filter whose color allows current to flow through the tube, you can begin to take your measurements.



Plotting the Results

A typical result for this experiment.

For the experiment itself, the object is to find some voltage, V, which will just prevent any current flow through the phototube. This is the stopping voltage, Vs which is just barely enough to prevent any electrons emitted from the anode plate from reaching the cathode wire. Plot this point on a graph showing voltage on the Y axis and the frequency of the filtered light on the X axis. Thus, you are generating a graph of stopping voltage (Vs) as a function of the frequency of the light reaching the phototube.

Note: The graph shown to the right does not necessarily match the results you would obtain from this experiment, although your results should be similar. The specific materials used in the phototube will have a significant effect on your measured and plotted results.

One interesting fact here is that once you have set the applied voltage to Vs, increasing the intensity of the light reaching the phototube (but not changing the filter) will not enable current to flow again. This is a key point. It demonstrates that each photon of a given frequency has exactly the same energy as every other photon of that frequency. Higher intensity means that more photons reach the target per second for more total energy delivered, but each photon still has the same energy as before.

Next, we change the filter to some other color and as before seek to find Vs for this particular frequency of light. Again, we plot this point on our graph. We continue this for every filter we have, and then fill in the spaces between our plotted points. If we've been careful enough with our measurements, we will find that the graph plots one of two ways. For all frequencies above a certain minimum, we have a straight line showing a linear relationship between Vs and frequency. Below that minimum frequency, there is no current flow at all, regardless of the applied voltage. If you did not use any filters for these frequencies, this cutoff frequency will not appear directly on your graph. However, you can find this point from your graph. The frequency at which Vs = 0 is the limit to which you can take this experiment; lower frequencies of light will not affect the phototube.



What it All Means

There are two basic factors that control the results of this experiment. First, it takes a certain amount of energy to free an electron from the surface of the metal anode of the phototube. This is known as the work factor. Second, the arriving light clearly imparts a certain kinetic energy to the freed electrons, which enables them to overcome the repulsion effect of the more negative cathode wire, and still cause a current to flow through the phototube. It is that kinetic energy that we are measuring when we adjust the applied voltage V to determine the precise value of Vs. Let's look at these two factors separately.


The Work Factor

When light energy reaches the metal anode, it may be sufficient to push an electron out of its orbit around its parent atom, and move it towards the surface. If this electron is from an atom at the surface of the anode, a certain amount of energy is still required to kick the electron away from the metal and let it fly through space. This energy is a measure of the amount of work required to remove the electrom from its initial environment. Therefore, it is known as the work factor of that particular metal.

Different metals have different work factors, but the work factor of any metal is a characteristic of the metal itself, and does not change for different frequencies of light. Thus, phototubes made of different metal materials will have different work factors, but the work factor for any given phototube will be constant in the experiment.

If the arriving light energy bypasses the first layer or two of atoms at the surface and then frees an electron, that electron will lose energy as it travels past other atoms before it is able to leave the surface. This electron will have less kinetic energy traveling through the vacuum of the tube than one released from a surface atom.

The work factor varies from about 2.2 electron volts (eV) for lithium to 6.35 eV for platinum. Any frequncy of light which cannot impart enough energy to the electrons in these metals to overcome the work factor will fail to cause a current to flow through the experimental circuit.


Measuring the Kinetic Energy of the Electrons

Once an electron has been freed from the surface, it is still moving, and therefore has a certain amount of kinetic energy. We can determine the kinetic energy of the most energetic electrons (often designated kmax) by determining the voltage needed to just prevent them from reaching the cathode of the phototube. The energy involved is then the product of the stopping voltage, Vs, and the electric charge on the electron. That charge is a fixed, known value, designated by the letter "e.". Thus, the product of the charge e and applied voltage V is designated eV and represents energy measured in electron-volts.

So long as we keep our energy units in eV, our experimental stopping voltage, Vs, is a direct measure of the energy needed to exactly cancel the kinetic energy of the free electrons, and hence of the energy imparted to those electrons by the arriving light.


Interpreting the Experimental Results

Although the exact measured results you get will depend on the exact material coating the anode of your phototube, your graph should turn out to be a straight line sloped to show that Vs increases with the frequency of the light used for that measurement. The general equation for this type of line is:

Y = mX + B

In this equation, m is the numerical slope of the line, and B is the Y-intercept. In this particular experiment, the general equation becomes:

kmax = eVs = hf - W

In this expression,
 
kmax is the maximum kinetic energy of any electron freed from the anode;
e is the charge on any single electron;
Vs is the stopping voltage at which conduction is just barely prevented;
h is a constant factor;
f is the frequency of light used in one particular step in the experiment;
W is the work factor of the specific material coating the anode of the phototube.

Even if your filters do not include the specific color whose frequency exactly matches the work function of your phototube's anode, you can extrapolate this value by extending your graph to the frequency (X) axis, which corresponds to Vs = 0. At this frequency, hf = W. Any light at a higher frequency can be used in this experiment. Light at a lower frequency cannot free electrons from the anode of the phototube at all; there is insufficient energy in such light, regardless of its intensity.

This inherent cutoff frequency varies according to the work factor of the phototube's anode, but always works the same way. As a consequence, it is not possible that light (or any electromagnetic wave) can have a continuously variable energy content. Rather, it must be made up of small "corpuscles" of energy such that each "corpuscle" either does or does not have enough internal energy to free one electron from the surface of the anode. More intense light at that frequency has more "corpuscles", but they all have the same amount of energy. If this last point were not true, the higher-energy "corpuscles" could still free electrons that lower-energy "corpuscles" could not affect.

These "corpuscles" are the quanta of electromagnetic energy, and are named photons.

The remaining factor that can be determined experimentally from the graphed results of this experiment is the slope of the line. This value turns out to be just about 4.135 × 10-15 eV·seconds — which is Planck's Constant. Since the freed electrons had a maximum kinetic energy of hf - W electron-volts, the energy in the photon that kicked the electron loose must have been E = hf. This expression relates the energy of the photon to its frequency throughout the electromagnetic spectrum.

The inescapable conclusion of this experiment is that light (or any electromagnetic radiation) is not a continuous phenomenon as originally believed, but rather is made up of discrete "bundles" of energy, now called photons, each of which exists independently of all other photons. It can give up its energy to a physical object such as an electron, but does not transfer energy to or from other photons or manifestations of energy. The energy content of the photon is proportional to its frequency (related by Planck's Constant), but is not controlled by anything else.


Prev: Characteristics of a Photon Next: The Transverse Electromagnetic Wave (TEM)

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