Title The Photoelectric Effect – Experimental confirmation concerning a widespread Misconception in the Theory Gao Shenghan 1, Huan Yan Qi 1, Wang Xuezhou 1, Darren Wong 2, Paul Lee 2 and Foong See Kit 2 1 Raffles Institution, One Raffles Institution Lane, Singapore 575954 2 Natural Sciences and Science Education, National Institute of Education, Nanyang Technological University, Singapore 637616 Abstract The photoelectric effect is a well-known and widely taught field in many schools and institutions, yet it has been shown through theoretical arguments that there is a common error in the theory in which this topic is learnt and taught.
The common theory is that the energy of the incoming photons must be greater than the work function of the emitter, and also that the difference between the energy of the photon and the work function of the emitter must be greater than the voltage applied between the emitter and collector multiplied by the elementary charge. This paper provides experimental evidence for the correct interpretation of the photoelectric effect in order to correct the misconception.
In this paper, it was experimentally determined that both the work functions of the emitter and the collector metals must be taken into account in order for a current to be detected, contrary to conventional theory. Introduction The photoelectric effect is the phenomenon in which electrons are liberated from matter as a result of electromagnetic radiation being shone onto it. Generally, the phenomenon is only investigated in metals as they require lower energy from the radiation. The photoelectric effect was first discovered by Heinrich Hertz in 1887 and was explained by Albert Einstein in 1905.
Einstein’s model quantized light as photons, each with energy E=h? where h is the Planck’s constant and ? is the frequency. Einstein also introduced the work function ? of a material, defined as the minimum amount of energy needed in order to liberate an electron from the material. Through this model, the characteristic photoelectric equation eVs=h? -? can be derived where Vs is the stopping voltage. Eisntein’s explanation and relations of the photoelectric effect, shown below, has been taught in many schools all around the world today and is widely known. Theory In this section we present the derivation of the photoelectric equation eVs=h? ?. From the definition of ? , it follows that once an electron has been liberated, it has a maximum possible kinetic energy of h? -?. This also implies that h? >? for a liberation of electron. When an external voltage V is applied across the metals, there is a potential difference between the plates and thus when the electron needs KE>eV in order to to reach the collector plate. Combining the two relations, we get h? -? >eV. In the equality case, we call the voltage Vs, which is the is the minimum amount of voltage needed to be applied such that no current is recorded. ‘Conventional’ understanding of the photoelectric effect: Alternative’ understanding of the photoelectric effect: The above section uses the work function ? e referred to that of the emitter material, even when the emitter and collector are made of different materials. However, this is incorrect, and the derivation is shown below: When an electron is just emitted from surface of the emitter, it has potential energy ? e above the ground energy state. Conversely, when an electron is just emitted from surface of the collector, it has potential energy ? c. Hence, if ? e?? c, we note that there will be a potential energy difference of ? c-? e, even if there is no external voltage applied.
This is known as the contact potential. ?c ?e ?c-? e Potential Energy Emitter Collector Figure 1: Energy diagram without an external voltage ?c ?e ?c-? e Potential Energy Emitter Collector Figure 1: Energy diagram without an external voltage Once a potential difference of V is applied between the two plates, there is an additional potential energy difference of eV. Collector ?e Potential Energy Emitter ?c ?c-? e+eV eV Figure 2: Energy diagram with an external voltage applied Collector ?e Potential Energy Emitter ?c ?c-? e+eV eV Figure 2: Energy diagram with an external voltage applied
Hence, in the process of calculation, the difference in potential energy of the two plates is not eV, but instead ? c-? e+eV. Thus, replacing this into the Einstein equation, we get eVs=h? -? c. Hypothesis The two requirements for a current to be detected in a photoelectric effect experiment are: 1. h? >? e 2. h? -? c>eV Instead of the commonly-quoted: 1. h? >? e 2. h? -? e>eV Objective To provide actual experimental confirmation of the proposed model, in addition to the currently-available purely theoretical arguments, in order to determine the correct explanation for the photoelectric effect Apparatus and methodology
Overview The experiment consists of a vacuum chamber with thin Zn and Ni plates placed close together but not touching. UV light was shone onto one of the metal plates and the resulting voltage between the two plates was measured. The materials of the emitter and the collector were changed, as well as the potential difference applied across the two plates. I-V curves were plotted and the results analysed. Experimental setup A cylindrical vacuum chamber at was pressure 1. 5? 10-2 mbars was used. The emitter and collector plate were placed in the vacuum chamber and were held up using polycarbonate discs, rods and metal rods.
The metal plates were placed with the surfaces parallel to each other at a fixed distance of 1. 0 cm apart. The surfaces of the plates were sandpapered after each trial. The overall setup of the circuit is shown in Figure 8. Crocodile clips were then used to connect the emitter and collector to the external circuit which can be seen in Figure 9. A window made of sapphire glass was constructed in order to let UV light enter the chamber (Figure 6). This was aligned with the metal plates such that the emitter received as much light as possible.
A UV light source was placed directly outside the sapphire window and shone UV light onto the emitter plate. The measurements from these two voltmeters will then be used to plot an I-V curve for each of the configurations: Zinc-Zinc, Nickel-Nickel, Zinc-Nickel, Nickel-Zinc. In each of the above cases, the emitter is named before the collector. Figure 3: Vacuum chamber 3 4 5 6 Figure 3: Vacuum chamber 3 4 5 6 Figure 6: Sapphire window used to let UV light into the chamber Figure 6: Sapphire window used to let UV light into the chamber Figure 7: UV Light used Figure 7: UV Light used Figure 4: Close-up of polycarbonate disc, rod and metal rod
Figure 4: Close-up of polycarbonate disc, rod and metal rod Figure 5: Close-up of the two metal plates Figure 5: Close-up of the two metal plates Figure 8: Overall view of setup Figure 8: Overall view of setup Figure 9: Circuit used for measurement of voltage and current Figure 9: Circuit used for measurement of voltage and current Wangxuezhou Results & Discussion Zn-Zn measurements Figure 10: I-V Graph for the Zn-Zn setup The nonzero photocurrent as measured at 0 V of applied voltage shows that the photon of the UV light has sufficient energy to cause emission of electrons from the Zn plate.
Therefore this implies h? >? Zn. In particular, we see that: h? -eVstopping? 6. 63? 10-341. 60? 10-193. 00? 108254? 10-9-1. 10 ? 3. 88eV ?? Zn Ni-Ni measurements The results for this setup produced values of zero photocurrent for all possible applied voltages. This means that the UV photon has less energy than the work function of Ni, in other words, h? <? Ni. Zn-Ni measurements Figure 11: I-V Graph for the Zn-Ni setup Negative values of voltage were not tested for this setup as voltages of 0. 30 V and lower already yielded a photocurrent of zero. Here, there is no current when V=0.
According to the conventional understanding, we need: 1. h? >? Zn 2. h? -? Zn>eVapplied When V=0, equation 2 reduces to h? -? Zn>0 which is identical to equation 1. Since we have already established above that h? >? Zn in the Zn-Zn experiment, thus a photocurrent is predicted to be present. However, there was no photocurrent measured, thus showing that the presence of a photocurrent is not solely dependent on the emitter. Now we consider the alternative understanding. We require: 1. h? >? Zn 2. h? -? Ni>eVapplied Here, equation 2 reduces to h? -? Ni>0. Since we have shown above that h? lt;? Ni from the Ni-Ni experiments, thus it is obvious that there would not be any photocurrent detected. Hence, the alternative understanding predicts the correct outcome. We can go one step further by predicting ? Ni. From our results, we see that a voltage of +0. 35 V is required for a photocurrent. From equation 2, we have: h? -? Ni=-0. 35eV. We then get ? Ni=5. 23eV which is close published values of 5. 15eV. Ni-Zn measurements Figure 12: I-V Graph for the Ni-Zn setup The Ni-Zn setup shows negative current from Zn to Ni some light were reflected off the Ni and turned it into a Zn-Ni experiment.
Once a sufficient positive voltage was applied, the negative current was unable to reach the Zn plate. Also, even though there is a large positive voltage, there is still no positive photocurrent detected, because the condition h? >? Ni is not satisfied. Conclusion This project has demonstrated experimental evidence of the theory that the work function of both the emitter and collector materials must be taken into account in order to predict the presence of a photocurrent. This refutes the well-known theory which only uses the work function of the emitter.
The experimental results also give values of ? Zn and ? Ni which are close to actual published values, indicating accurate experimentation. In conclusion, the conditions for a photocurrent to be produced are: h? >? e and h? -? c>eV Acknowledgements The group members would like to thank their mentors for their continued guidance and support throughout the course of this project. They would also like to thank Ms. Cecelia for her help in the experimental preparation. Last but not least, the group members also thank their teacher-mentor in Raffles Institution, Ms.
Kek Ai Kiew for her help and guidance for this project. References [1] Young, H. D. , Freedman, R. A. , & Ford, A. L. (2008). Sears and Zemansky's University Physics 12th edition with modern physics. San Fransisco, California, United States of America: Pearson Addison-Wesley. [2]Einstein, A. (1905). Uber einen die Erzeugung und Verwandlung des Lichtes betreffenden heuristischen Gesichtspunkt. Annalen der Physik, 17, 132–148. [3] Nobelprize. org. (2010, July 12). The Nobel Prize in Physics 1921. Retrieved from http://nobelprize. org/nobel_prizes/physics/laureates/1921/index. tml [4]James, A. N. (1973). Photoelectric effect, a common fundamental error. Physics Education, 8(6), Retrieved from http://iopscience. iop. org/0031-9120/8/6/005 doi: 10. 1088/0031-9120/8/6/005 [5]Rudnick, J. , ; Tannhauser, D. S. (1976). Concerning a widespread error in the description of the photoelectric effect. American Journal of Physics, 44(8), 796-798. [6]Barbalace, K. (2007, February 22). Environmentalchemistry. com. Periodic table of elements: Nickel (Ni). Retrieved from http://environmentalchemistry. com/yogi/periodic/Ni. html
