The Photoelectric Effect

One of the most revolutionary concepts in physics is the photoelectric effect. The photoelectric effect occurs when radiant energy is impinged on various metals and electrons are ejected from the metal surface.  The ejected photoelectrons have a certain kinetic energy which can be measured by the produced voltage.  Photoelectric current cannot be explained by the wave theory as diffraction and interference can, however.  The photoelectric effect is important because it revealed some of the limitations of the classical wave theory and it gave closer insight into the nature of light- namely the quantization as photons.

Our experimental setup, consisted of a high-intensity mercury lamp, a vacuum photodiode, an electrometer, and different light filters.  We wanted to accomplish two goals in this lab.  First, to observe the change in photoelectric energy as light frequency changed and second, to observe the change in energy as the light intensity changed.  A sketch of the apparatus follows:

For all of our measurements, we first zeroed the electrometer.  This was important because the electrometer tended to drift.  We used an electrometer instead of a standard voltmeter because the photocurrent produced by the phototube is very small and a voltmeter consumes a small amount of current (about 0.1ua at 1.0V) whereas an electrometer consumes no current.  Following is a picture of an electrometer:

Before taking measurements we also made sure that the phototube was in brightest stream of light and the anode was shielded from the mercury lamp.  It was important to line up the shadow mask or else the radiant light from the lamp would hit the anode, causing electrons to be ejected from the anode, basically canceling out our desired effect.  Even with our caution, some light did hit the cathode and, without ejecting electrons, hit the shadowed part of the anode.

For our particular measurements, we used a blue (436 nm), green (546 nm), and yellow (577 nm) filter:

Additionally, we used a glass (365 nm) filter and a laser beam (~630 nm).  [In an attempt to relate our research to the common person, we used a sunglasses lens- the results are inconclusive, unfortunately.]  The frequency of each reading was calculated by relating the speed of light and wavelength.

                                    Blue (436 nm)                                                           Green (546 nm)
                                      V= -1.21                                                                      V= -0.77
                   (c/l)= f = (2.997e8m/s)/(4.36e-7m)                                (c/l)= f = (2.997e8m/s)/(5.46e-7m)
                                = 6.87e14sec-1                                                              =5.49e14sec-1

                            Yellow (577 nm)                                                        Glass (365 nm)
                                        V= -0.77                                                                    V= -1.79
                    (c/l)= f = (2.997e8m/s)/(5.77e-7m)                             (c/l)= f = (2.997e8m/s)/(3.65e-7m)
                                 = 5.14e14sec-1                                                            = 8.21e14sec-1

                                                                     Laser (~630 nm)
                                                                           V= -0.43
                                                                  (c/l)= f = (2.997e8m/s)/(6.30e-7m)
                                                                               = 4.76e14sec-1

The voltage readings from each of these measurements was used in a plot of photovoltage vs. frequency.  The slope of this graph provided us the (h/e) ratio which was used to find Plank’s constant.  It is important to note that through this relatively simple experiment, a good approximation of Plank’s constant and the work function (f) for the cathode were determined.

(From Graph)         -3.78e-15 vsec x  1.6e-19 J = (-)6.05e-34 Jsec = h
                                                        (8.3% error to literature value of 6.6e-34 Jsec)

The second section involved examining the effects of intensity on the photovoltage reading.  Basically, we doubled the distance between the mercury light source and the phototube and observed voltage change over time.  Essentially, the low intensity curves had a more gradual rise to equilibrium but they still reached the same point as the high intensity curves.  This showed that the number of photoelectrons decreases with intensity but all photoelectrons within the same wavelength have the same energy.  A sketch of observations follows.  The high intensity (bright) appears above the low intensity plot (dim).

This result disproved the wave theory’s prediction that a smaller intensity produces a smaller photoelectric energy.  As Einstein asserted, photoelectric energy is independent of intensity and can only be affected by frequency change.  Furthermore, he stated that every electromagnetic wave of frequency f, is actually a stream of energy quanta and a photon is one quantum of light.  This conclusion challenged the wave theory and forced the particle nature of light to be considered.

Some Links of Interest:

 The Photoelectric Effect in Plain English

 Photoelectric Effect Applet

 Photoelectric Effect Apparatus Ordering Information

 Brown University Lab Instructions for Photoelectic Effect Experiment