BACKGROUND

The photoelectric effect is simply the ejection of electrons from matter by incident electro-magnetic radiation, particularly visible light, ultraviolet light, and x-rays. At the time of the discovery of this effect in the late nineteenth century, however, it seemed anything but simple; in deed, the observed nature of this process contradicted much of what was known about electromagnetic waves. In the end, a considerable upheaval in classical physics resulted, but it was more of the nature of a great expansion and improvement, rather than a demolition, of what had gone before.

One of the first published observations of this phenomenon was by Heinrich Hertz, who, while conducting some of his monumental studies of electromagnetic waves in 1887, noticed that the gap between a pair of oppositely charged electrodes broke down, or sparked, quite readily when a second spark gap was fired in the immediate neighborhood. He verified that ultra-violet radiation, i.e., waves somewhat shorter than those of visible light, was irradiating the first gap and causing it to break down.

Subsequent research by others in the next few years produced the following results:

A) A clean, insulated zinc plate was found to become positively charged when irradiated with ultra violet light -- even in a vacuum -- and a negatively charged plate lost its charge when so illuminated. (W. Hallwachs, 1888) B) The electron had, during this era, been identified, and its charge-to-mass ratio measured by J. J. Thomson. It was shown that the acquisition of positive charge (and the loss of negative charge) by irradiated plates was in fact due to electron ejection. (P. Lenard, 1900) C) The first of the fundamental laws of the photoelectric effect was announced by J. Elster and H. Geitel in 1900. Their apparatus consisted of a pair of plates in a vacuum, one of which was irradiated. The second plate was positively charged, and thus attracted the (negative) electrons to itself. This transfer of electrons between plates was read as an electrical current in an external circuit. It was shown that the electrical circuit current, and hence the number of photo-electrons ejected per unit time, is exactly proportional to the intensity of illumination. One may express this as

N = I ,

where N is the rate of electron emission, and I is the intensity of the ultraviolet light. The constant

depends on the material of the emitting plate, or photocathode, its surface condition, and the wave length and angle of incidence of the radiation.

D) In 1902, P. Lenard arrived at the second, and most astonishing law of the photoelectric effect. Before stating it, let us make some predictions, based on classical electromagnetism, about what we expect the energy of the ejected electrons to be, or more specifically, how we might expect their energies to vary as we change the intensity of the ultra violet light.

You will recall that an electromagnetic wave consists of oscillating electric and magnetic field at right angles to each other and also to their direction of propagation. The intensity of the wave is proportional to the square of the electric (or magnetic) field strength, i.e.,

,

Now, it is reasonable to suppose that the electric field is what tears the electron loose from the metal surface; no other process in fact, can do the job. Therefore, it should be equally reasonable to expect that the speed of the ejected electrons should be greatest for the most intense irradiation.

Lenard measured these electron speeds by applying a small negative, or repelling, voltage to the collector plate in his apparatus. We illustrate the principle in Fig. 1.

Figure 1

If an electron is ejected from the cathode with a kinetic energy V= , and if it finds itself in an electric field parallel to its velocity, it experiences a decelerating force

,

since its charge is negative. Now, the electron does work in moving against the force, and this work comes out of its kinetic energy. Thus,

,

and so, when the electron reaches the anode,

= ,

since .

Clearly, the electron will be turned back before it reaches the anode if

eV > .

Thus, we have a means for measuring electron kinetic energies: simply apply a retarding potential and measure the resulting circuit current. When the current just disappears, we have applied a voltage corresponding to the most energetic electrons. This means of measuring charged particle energies (and also of accelerating, rather than decelerating them) is so common that it is now universal practice to specify particle kinetic energies in electron volts. An electron which is just stopped at the anode of the apparatus by a one volt retarding potential had an initial kinetic energy of one electron volt (eV).

Now, Lenard used exactly this procedure to determine the distribution of electron energies from a photocathode. He came forth with a most surprising result, which was that the maximum electron kinetic energy depends only upon the wavelength of the irradiation and is completely independent of its intensity.

E) The dependence of maximum electron energy on wavelength was found to be extremely simple (Millikan, 1916). It is stated most simply in terms of the frequency of the light, which is

,

where c is the velocity of light ( = 3.0 x 1010 cm/sec), and is the wavelength. Then the experimentally observed relation is given by the following graph of maximum electron energy vs. frequency:

Figure 2

The curve is a straight line of the form

,

or,

.

But this relation is exactly one announced by Einstein in 1905, on purely theoretical grounds. Einstein's main supposition was based on an earlier idea of Max Planck, the interchanges of energy between matter and radiation occur in discreet bundles or quanta of energy. Each quantum was asserted to contain energy in proportion to the radiation frequency, i.e.,

W = hv;

the constant h has ever since been known as Planck's constant. The Einstein relation sees that the kinetic energy of an ejected electron should be equal to the quantum of energy less the energy Wo which is an amount which must be spine to get the electron loose in the first place. This equation suggests -- and indeed, experiment has shown -- that Wo depends upon the material and condition of the photocathode, but the constant h is always the same. What is also implied is that unless the frequency v is greater than vo ( = Wo/h) for the particular material, no photoelectrons will be ejected. This is found to be precisely true. The work function, Wo , varies greatly from one substance to another. For the alkali metals, photoelectrons can be produced by visible light; photocathodes containing cesium are commonly used on vacuum photocells such as the one you will use in this experiment.

F) From the form of the Einstein relation, one might surmise that the quantum of energy has at least some of the attributes of a particle whose kinetic energy is hv, and which somehow collides with the electron, knocking it loose. It turns out one other important observation lends great strength to this idea.

Let us consider the consequences of applying classical electromagnetic theory to photoejection of electrons for the case of very weak incident illumination. One of the standard results of the wave theory of radiation is that the energy flux (i.e., the wave energy passing through unit area normal to the beam each second) is uniform over a plane wave front, and that this flux is a direct measure of the intensity; it varies as E2 , as we mentioned above.

Now, while some information about the density and atomic weight of the cathode, and also about the depth of penetration of the radiation, we can make an order-of-magnitude guess about the number of electrons on each square centimeter (or meter) of the cathode which are available for ejection. If this Number is, say, ns electrons per cm2 , then each electron can receive its share of the wave energy from an area no bigger than l/ns cm2 .

Suppose, in c.g.s. units, we assign a beam intensity of

I ergs cm-2 sec-1.

Then, each electron can get energy no faster than

I/n s ergs sec-1

If the work function, i.e., the basic ejection energy of the electron is Wo , then, in order to get out, the electron has to accumulate energy for a time of

seconds.

In the face of all this, it has always been observed that the time delay between the start of illumination and the appearance of photoelectrons is unmeasurably short, even when , as estimated above, is many days.

What must be true here is that the energy distribution in the wave front is not uniformly distributed, but on the contrary, highly concentrated at particular points.

All of these observations give very heavy support to the notion that light really consists of small packets of energy, (which have come to be called photons) each of which carries energy hv. Variations in light intensity are then no more than variations of the flux, or stream density, of these particles; hence, the results that the photoelectric current is exactly proportional to light intensity. The energy of ejected electrons is now obviously independent of intensity, since a particular electron is set free by only one photon. Furthermore, the fact of one-photon-per-photoelectron also makes the duration of the ejection process quite independent of the photon flux.

However, there still remains, in spite of the foregoing, a great dilemma concerning the nature of light. While photoelectric phenomena absolutely demand a photon concept, other equally certain observations, such as the diffraction and interference of electromagnetic radiation are only sensible in a wave picture. This problem has been resolved by the quantum theory which was developed after 1925. It is beyond the scope of an elementary course, however, and for now we must leave this "duality" as a tantalizing intellectual puzzle.