Photoelectric EffectMichael Angelo A. Racelis1, John Lorenzo M. Reyes 1*, Thor Jason Roi T. Tenefrancia1, and Rock Christian V. Tomas 11Department of Electrical Engineering- CEAT, UP Los Baos*Corresponding author: johnlorenzoreyes@gmail.com

Abstract The experiment aims to determine the effect of the frequency and intensity of light, on a given metal surface, to the photocurrent produced. Other quantities such as the cut-off frequency were also derived. The relationship of the current produced and the wavelength of light were graphed such as the relation of the stopping potential and the light frequency. As for the set-up, a black box containing the metal was used to study the phenomenon with a lamp as the light source and a voltmeter and an ammeter to measure the current produced and the stopping potential respectively; color filters were used as to change the lights frequency. The group concludes that an increase in the frequency of light amounts to an increase in the maximum current attainable, given that the energy of the light is greater than that of the metals work function, while the intensity is to the magnitude of the photocurrent produced. Graphically, the potential-frequency equation is a linear equation with a positive slope.Keywords: cut-off frequency, photocurrent, work function

I. Introduction

During the mid-century of the nineteen hundredths, James Clerk Maxwell formulated four equations that stand as the foundation of electromagnetic theory. While the equations were successful in modeling various phenomena concerning electromagnetic waves, such as those that appear in magnetism, circuit theory, and ray optics, it was unable to explain others; one of these phenomena is the photoelectric effect.

The photoelectric effect is a phenomenon where in an electron is emitted from a surface when such surface is illuminated by a light of certain frequency. This phenomenon was explained by Albert Einstein, which earned him his Noble Prize. Einstein, taking Max Planks quantization idea into account, described a ray of light composed of photons in the quantity of the Avogadros number. In his winning paper, he depicted light not as a wave but as a particle (photon), interacting with the electrons such as billiard balls in a pool table. Given the assumptions Einstein was able to explain the various experimental observations that Maxwells equation failed to perceive, such as why a red light could never release photoelectrons given a certain metal sample, while a blue light is able.

The experiment aimed to explain various experimental observations through using the photon theory of light. The effect of the intensity and the frequency (color) of light to the photocurrent produced was also addressed. Furthermore, given the frequency and the data provided through the experiment, the Plancks constant was derived and so as other parameters such as the maximum electron kinetic energies. The group hopes to further validate the photon theory of light through such experiment; a theory which is the foundation of numerous technological innovations today, such as solar panel technology, night vision, sensors, and many more.

II. Methodology

The researchers set up the materials according to the image shown to them. They turned on the light source for 15 minutes before performing the experiment in order for the bulb to attain thermal equilibrium. They positioned the light source 3 centimeters away from the filter. The light from the light source was blocked before placing the filter into the opening of the Photoelectric Effect setup. Then, the researchers turned the VOLTAGE knob to zero. They adjusted the ZERO knob until the pointer of the nano-ammeter reads zero. Then, the cover was removed and the researchers adjusted the VOLTAGE knob until the current reads zero. The researchers then recorded the voltage in Table 1.1. Then, they lowered the voltage until they get a maximum current reading and divided the difference of it and the voltage that zeroed the current into ten parts. Each part they recorded the current reading in Table 1.1 also. The researchers repeated the procedure for all color filters until Table 1.1 was completely filled out where all observations are repeated in three trials and the researchers get the average. Then, the researchers plotted the I-V curve for each light color in Figure 1A. And then, they recorded the stopping potential, the voltage at which the current reads zero, for each color in Table 2.2. The researchers then plotted the stopping potential against the frequency of light in Figure 1B. And they performed linear regression of the stopping potential frequency plot and they computed for the slope and y-intercept.

nAVzerovoltage

+ -Figure 1.1. Experiment setup

III. Results and Discussion

Upon conducting the experiment, it was observed that light intensity has an effect on the photocurrent. This phenomenon was seen when an object accidentally blocked the light source on the ceiling from the instrument on the setup and the current reading on the instrument decreased. When the object moved away from the setup, the current reading increased. Hence, it can be said that as the intensity of the light increases, the photocurrent increases.

Based on Figure 1.1A, it can be inferred that current decreases with increasing voltage. The statement holds for every wavelength of light used in the experiment. Also, it can be observed that the magnitude of the current is independent of the wavelength of the light used, as most of the observations for current have approximately the same range of values. The physical quantity represented by the slope of each respective graph represents the conductance (-1) of the conductor used.

From the experiment, the cut-off energy of red light averages 0.4237 V, 0.669 V for green light and for blue, 0.8137 V. We can say that lower frequencies of light, has lower cut-off energy. Hence, the cut-off energy of light is directly proportional to its frequency.

Figure 1.1A. IV Characteristics at different wavelength of light.After finding the best-fit line of the voltage-frequency curve, the researchers obtained this equation: y = (2.1705 x 10-15) x 0.6102, where y is the stopping potential, V0, x is the frequency of light and 0.6102 is the work function of the metal used in volts. This equation is from eV0 = hf , dividing both sides by e results into V0 = (h/e) f /e. Therefore, the ratio h/e in the experiment done is 2.1705 x 10-15 Weber, since h is in Js and e is in C, then h/e is in Js/C = J/A = Wb.

The physical quantity which the slope represents is the Plancks constant divided by the charge of an electron (e -). Knowing that the slope of the graph is constant, it can be inferred that stopping potential has a linear relationship with the frequency of light. Based on the experiment, the computed value of Plancks constant, after converting is 3.478 x 10-34 Js which has a percent error of 47.52%.

Due to the presence of flowing current, as measured by the ammeter, it can be determined that there are moving electrons. The electrons are moving due to energy absorption from the photons beamed onto the conductive surface where they are found. The nature of the absorption follows the law of conservation of energy.

Figure 1.1B. Stopping voltage versus the frequency of light, excluding the wavelength of white light.

Since minimum amount of energy to remove an electron from a surface is equal to work function, we can write Einstein equation as:

Energy Supplied = Energy Consumed in ejecting an electron + maximum Kinetic energy of electron

It is known that the slope is equal to the value of Plancks constant. Recall that Einstein proposed that the energy of a photon is equal to the frequency multiplied by Plancks constant.

Since and , Since ; ,

Rearranging and substituting,

This equation can be used to determine the relationship of stopping potential with frequency, as illustrated in the graph above.

From the experiment, the kinetic energy of red light averages 6.7879 x 10-20 J, 1.0719 x 10-19 J for green light and for blue, 1.3036 x 10-19 J. Photoelectrons produced by different color of light have different kinetic energy. This is supported by the equation Kmax = eV0 = hf = hc/ , where is the work function of the metal that is subjected to the photoelectric effect. Thus, longer wavelengths of light yield photoelectrons with lower kinetic energy.

Also, even if a more conductive metal is used, the slope would remain the same because its value is equal to that of the value of Plancks constant.

IV. ConclusionBased on the results of the experiment, the light intensity is directly proportional to the photocurrent. Moreover, the cut-off energy of light is also directly proportional to its frequency. Also, it was found that a lights wavelength determines the level of kinetic energy that the photoelectron. A photoelectron with low kinetic energy yielded from light with a long wavelength. Plancks constant was also obtained through acquiring the slope of the stopping voltage versus light frequency graph. The experimental Plancks constant obtained was 3.478 x 10-34 Js and had 47.52% as its percent error. Also, the ratio h/e is the computed magnetic flux since the dimensions it gave was J-s/C or Wb.

For the people who are about to repeat the experiment, the researchers recommend to turn off the light if all trials will also be performed with the lights off. Otherwise for consistency, it is recommended that the environmental conditions for the initial trial be followed for the rest of the experiment.

References: 1. H. Young, R. Freedman, University Physics, Chapter 40, Addison-Wesley of Pearson Education, Inc. CA, 2012. Pp 1232-1236.2. Notes on Professor Anthony Allan D. Villanuevas Lectures