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THE PHOTO-ELECTRIC EFFECT INTRODUCTION This is one of the fundamental experiments of quantum physics. It utilizes the phenomenon of photo-electric emission of electrons and provides a simple h way to determine , the ratio of Planck's constant to the electronic charge. e The optical arrangement of the apparatus used is shown schematically in Figure 1. A picoammeter and a variable voltage source are also provided. The equation of conservation of energy that describes the production of photoelectrons is Hv = Kmax + W (1) Where v is the frequency of the light incident on the photo-sensitive surface, Kmax is the kinetic energy of the most energetic electrons emitted from the surface and W is the work function of the surface. The emission of electrons from the cathode produces a photo-current that can be measured with a picoammeter (see Figure 2). If the anode is maintained at a negative potential V with respect to the cathode, the photo-electrons will experience a retarding field. Thus as V is changed the photo-current will be changed, and there will be some value Vs of the anode potential which stops the most energetic electrons and reduces the photo-current to zero. Thus. Kmax = eVs (2) Combining equations 1 and 2 Vs h W v e e (3) h In principle then, by determining Vs as a function of v, is obtained as the e slope of the graph of Vs versus v. THE EXTPERIMENTAL SET-UP The apparatus is mounted on two optical benches. (See Figure 1 for a schematic representation.) The first part of the apparatus consists of a mercury lamp and some optical devices including a constant deviation prism to produce dispersion of the mercury spectrum. When the light emerges from the prism the mercury spectral lines are sufficiently dispersed so that any single spectral line can be made to focus on the photo-cathode. By moving the first optical bench with respect to the second the photocell can be exposed to a small portion of the spectrum. Thus the apparatus should be set up to focus a spot of monochromatic light on the photo-sensitive surface. This spot should spread over a sizeable region of the photo-cathode but should also be sufficiently small so that light does not hit the anode ring. (The American Institute of Physics Handbook lists the wavelengths and relative intensities of the mercury spectral lines.) In setting up the apparatus the photocell should be kept in the light-tight box until all adjustments are completed. Replace the photocell with a sheet of paper while arranging the apparatus so that a spectral line is focused on the spot where the photo-cathode will be. The photocell should never be exposed to any light except under these experimental conditions. Room lights should be turned off when the photocell is out of its box. The apparatus should be arranged electrically as in Figure 2. The Keithley 414A picoammeter is a sensitive ammeter which permits measurements of currents, with a maximum sensitivity of 100 pA full scale. The "Bias Potential Box" provides the stopping or accelerating potential to the anode. (The anode can be made positive with respect to the cathode if A and C are interchanged.) The voltage V is not simply the potential difference between anode and cathode but includes some (small) voltage drop across the picoammeter - note that photo currents will range between ~1 A and ~1pA. Measure the photo-current as a function of retarding voltage. If there is a back current, i.e., there is a current when the anode potential is more negative than Vs, some corrections may have to be made in the data. This is discussed in the Melissinos reference. You should obtain values for Vs for a number of h spectral lines, and determine using equation (3). e SUBTLETIES This experiment is in fact considerably more complicated than is implied in the simple description above. It is probably a commendable achievement to h obtain a value for within 5% of the accepted value, although the total e uncertainty in the experimental values is ~1%. A crucial difficulty with the experiment is the anode current that almost always exists. (see e.g., "Evaluation of Commercial Apparatus for Measuring h/e", Amer. Jour. Physics 34, 75 (1996)). It is difficult to decide whether the best procedure is to attempt to eliminate this reverse current, or to make some correction for it. You will have to put considerable thought into how you assign a value of Vs from the V-I plots which probably won't simply have I go to zero and stay there below some value of V. Another difficulty lies in the choice of mercury spectral lines. When the spectrum contains two or three closely spaced lines, it is the highest frequency line (rather than the most intense line) that dominates the V-I plot in the region of Vs. In fact, of course, the experimental V-I data is the sum of the photo-currents produced by each line. This problem is greatly diminished when the most intense line of the group is also the highest frequency line. A common source of difficulty is electrical noise pickup. Careful separate grounding of the cell housing and the bench reduces this noise. However, any capacitive pickup by the unshielded part of the sensitive picoammeter lead will produce problems. Care of the photocell is an important aspect in the obtaining of good results. Electrically conducting salts deposited on the glass surface by handling may cause leakage currents. Also, light exposure may affect the work function of the cathode surface, either reducing that work function or making the surface non-uniform. The real challenge of this experiment lies in understanding the many nontrivial processes that complicate the simple picture described by equation (1). REFERENCES Melissions, Experiments in Modern Physics American Institute of Physics Handbook "Evaluation of Commercial Apparatus for Measuring h/e", Amer. Jour. Physics 34, 75 (1996).