PhET’s Photoelectric Effect Simulation: Experiments and Analysis for Classroom Practice

This paper describes the use of the PhET simulator on the photoelectric effect to explore the behavior of electrons in metal when exposed to light with differing frequencies. Using this simulation, students can be able to observe variations in electron emission when changing various parameters such as intensity or frequency of light. This paper is experimental research to test the PhET simulator on the photoelectric effect in terms of the guiding relationship in the photoelectric effect. This also analyzed the PhET simulation for improvements in classroom activities. The main tool of this research is a computer capable of running the PhET simulation. It was found that all principles of the photoelectric effect are followed by the simulation. This includes if there is an emission of electrons, the relationship between the kinetic energy of the electron and frequency, and the relationship photoelectric current and light intensity. However, it was observed that there is no work function of the metals on the simulation and this can have an effect the prediction if there is an emission or not. The graphs generated of the simulation contains error because of the thick line graph. It would be better for classroom practice if these gaps are bridged and teachers manage to adopt the simulation.


INTRODUCTION
The photoelectric effect is a phenomenon in which electrons are released from a metal or semiconductor material when exposed to light or other forms of electromagnetic radiation. In simple terms, when a photon of sufficient energy strikes the material's surface, the photon's energy is transferred to an electron that is bound to the material and this electron can escape from its bond, causing it to be released from the surface and becoming free.
The key insight behind Einstein's explanation of the photoelectric effect was that light had to be considered as composed of discrete packets of energy called photons instead of waves, contradicting previous theories (Rodgers, 2019). Einstein proposed that each incoming particle contained a certain amount of energy that was both independent of its intensity and proportional to its frequency-the higher the frequency, the greater the energy carried by each packet, with no upper bound. This idea showed that metals respond more intensely to high-frequency light than low-frequency light. Despite being revolutionary at the time, this theory has since been widely accepted in science today (Masters, 2021).
To do a photoelectric effect experiment in the classroom, students will need to gather several materials, including a metallic plate, an electrode, an external light source, and a current meter or analog voltmeter (Cai et al., 2021). The plate should be connected to the electrodes with wires, and then exposed to the light source held at a steady distance. The voltage of the surface of the metal plate should be monitored using the current meter or voltmeter. As the intensity of the light source is increased, students can note any increases or decreases of voltage on the surface of the metal plate. If ultraviolet light is used instead of visible light, more pronounced fluctuations in voltage are expected. Finally, once experiments are complete, students can observe how their results match their expectations based on theoretical predictions regarding how intensities and wavelengths of light influence electrons jumping from metal surfaces.

Research Problem
The problem with conducting the photoelectric effect experiment in the classroom is that it requires sophisticated materials which may not be available in the classroom laboratory (Ješková & Kozelková, 2022). To solve this issue, teachers use simulations like the PhET Interactive Simulations of the University of Colorado Boulder. The photoelectric effect can be simulated using Phet Simulations by providing an electric field, which will cause the electrons to be either repelled from the negative end or attracted towards the positive end. By manipulating different parameters such as the frequency of incident light, the intensity of light, and the work function of the material, users can observe how it affects the kinetic energy of freed electrons. Further, this simulation allows users to modify voltage levels applied to a metal plate and calculate stopping potential with the help of Ohm's Law. Additionally, they are allowed to take multiple readings to conclude the photoelectric effect.

Research Focus
The objectives of this study are: 1) calculate the photoelectron kinetic energy from various types of metal; 2) determine the relationship between current and light intensity; 3) calculate the gradient of the graph of photoelectron energy against frequency; and 4) analyze the errors of PhET's photoelectric effect generated graphs for improvement of classroom practices.
Errors may arise from the simulations, Dasmo, et al (2019) computed Planck's constant with a 0.15% error from the PhET simulations. Some simulations may give incorrect answers to user input, leading to inaccurate results that could impact student learning outcomes (Bellotti, et al., 2010). In some cases, there may be too few customization options available for a given simulation type, resulting in a limited range of activities or ideas that can be explored by students (Wohn, & Wash, 2013).
The photoelectric effect equation states that the kinetic energy of the liberated electron from a metal surface is proportional to the frequency of the incident radiation and is independent of the intensity of this radiation (Liana, 2020). This equation can be expressed mathematically as: (1) where KE is the kinetic energy of the photoelectron, h is Planck's constant, f is the frequency of light sources, and  is the work function of the metal.
Equation 1 implied that as the frequency of the light source increases, so does the energy of the photoelectrons release, which also increases their velocity and kinetic energy. This means that electrons can escape from their atoms and become free electrons using only moderate levels of energy.
If equation 1 is graphed analogous to a straight-line graph, the y-axis is KE and the xaxis is the frequency of the light sources. So, the gradient of the graph, the kinetic energy of the photoelectron against the frequency of light sources is Planck's constant which is equivalent to 6.63 × 10 -34 m 2 kgs -1 . The intercept of this graph is the work function of the metal.
The wave equation is c = f, by which c is the speed of light, and  is the wavelength of light. Therefore f = . Substituting this to equation 1.
The energy required for an electron to escape from its binding metal surface can vary from material to material, but this variation does not affect the relationship between frequency and kinetic energy when an amount of light with a certain frequency shine on it. If a light has a lower frequency than a metal's work function, then no electrons will be liberated regardless of how intense that light may be. However, if enough light with sufficiently high frequency strikes the metal's surface, electrons will be released with corresponding increases in their kinetic energies-an effect known as the photoelectric effect.
From equation 2, the photoelectron energy is directly proportional to the frequency of the light source, and inversely proportional to the wavelength of the light source. This means that more energetic, higher frequency light produces more energetic photoelectrons with greater kinetic energy. Conversely, lower frequency, less energetic light produces photoelectrons with lower kinetic energies. Moreover, the energy E of the photon can be calculated using: When this energy strikes the metal, the total energy of many photons (N) is: E = Nhf (4) The photoelectric current (n) is defined as the number of photons incident per unit of time, hence n = The general equation for Power (P) is that it is equal to energy per unit time. So, the power is P = Substituting equation 5 to 6 P = nhf (7) Therefore, the photoelectric current equation is There is a need to connect the intensity to the photoelectric current. The intensity (I) of light source is where A is the incident area of light. Power based from this intensity equation is IA. Finally photoelectric current equation is n = (9) From equation 8, the photoelectric current is directly proportional to the intensity of light. This means that as the intensity of light increases, the photoelectric current also increases proportionately. When the intensity of the light increases, more electrons will be freed from the material, resulting in a greater flow of current. Higher-energy frequencies tend to produce more photoelectrons than lower-energy ones, and so higher-frequency lightslike those with a shorter wavelengthusually provide higher levels of current (Gupta, et al., 2021).

General Background of Research
This research was conducted inside the Physics Laboratory of the Presidential School of Uzbekistan in Qarshi City. The main material used was the MacBook computer which could run the PhET simulation of the photoelectric effect. There are system requirements required. Phet simulations are developed using HTML5 and run in browsers such as Chrome, Firefox, Safari, Edge, and Internet Explorer. It requires an up-to-date browser, with the latest version of Adobe Flash installed. Additionally, it may require Java or QuickTime to be enabled in your browser.
The methodology is a pure experimental method. The variables are discussed in the procedure. Erath, et al (2021) emphasized that a pure experimental method is a research approach that involves manipulating an independent variable and observing the effects on a dependent variable while controlling for extraneous variables. Pawar (2020) argued that the pure experimental method is a rigorous research approach that allows researchers to establish causal relationships between variables. However, it can be challenging to implement in practice due to limitations such as ethical constraints, cost, and feasibility.

Subject of Research
There are no students or subjects involved in this research. This paper was conducted to test the PhET simulation of the photoelectric effect of its effectiveness in terms of the guiding principles of the said law in physics. The simulation was also analyzed, especially the graphs, for teachers to be directed on which parts are good for experiments and which parts they need to adjust due to some errors in simulations.

Instrument and Procedures
To start the simulation the user should follow these details: 1) first, go to phet.colorado.edu and click on the -Photoelectric Effect‖ simulation; 2) in the left-hand pane, select -Controls‖ to configure your simulation variables such as wavelength, intensity, and material type; 3) adjust the controls accordingly to observer the effects of each on current and voltage readings from the simulator's graph at the bottom of the window; 4) In addition to these controls, you can also set up a demonstration mode by selecting -Show‖ in the left-hand pane and then click on one or more demonstrations for an enhanced learning experience with videos and other interactive components; and 5) lastly, you can use the -Graph Inspector‖ which allows manipulating of both current and voltage graphs simultaneously to observe their behavior in real time as you adjust controls.
The first experiment is to measure the photoelectron's kinetic energy from various types of metal. The independent variable is the frequency or wavelength of light source while the dependent variable is the photoelectron's kinetic energy. The control variables were the work function of the metal and the type of metal. Shown in Figure 1 at the upper center, the wavelength can be varied by sliding the wavelength control bar either to the left, to increase it, or to right, to decrease it. The kinetic energy of the photoelectron was calculated using equation 2. The second experiment is about photoelectric current and intensity of the light source. The independent variable is the intensity of the light source. In the Phet simulation, this is counted a percentage. The user can slide the intensity control bar to left and right to decrease and increase the intensity respectively. There were seven intensities counted. The dependent variable is the photoelectric current. This is observed from the digital bar on the lower center portion of the simulation. The control variable are type of light source and type of metal.

Data Analysis
The graph of the kinetic energy against frequency was plotted. The kinetic energy on the y-axis and the frequency of light on the x-axis. The gradient of this graph is the Planck's constant. The graph of kinetic energy against frequency generated from the Phet was considered as well to compute the Planck's constant. There is an indication that an error is found on the graph since the line used is too thick. The error was computed as percent error using the formula: % error =| | . The EV is the experimental value and ST is the standard value. The standard value of the Planck's constant is 6.63 x 10 -34 Js. The higher the % error means that there is a big gap between the experimental value and the standard value.
Based on experiment 2, the graph of photoelectric current and intensity of the light source was plotted. The photoelectric current on the y-axis and intensity of the light source on the x-axis. The gradient of this graph is .

Photoelectric Effect on Various Types of Metal
There are five different types of metals that can be found in the PhET simulations namely: sodium, zinc, copper, platinum, and calcium. This can be located in the upper right corner as shown in figure 1. The experiment used only two metals and the basis is lottery method. To measure the kinetic energy of the photoelectron, equation 2 was used. Again, the independent variable in this experiment is the wavelength and the dependent variable is the kinetic energy.
The photon energy was calculated using equation 3. When photons are incident on a metal's surface, they can transfer enough energy to an electron bound to the atoms in the metal surface, that it can break away from its bonds and be emitted. This process occurs as long as the energy of each photon is equal or greater than the work function energy required to remove an electron from its binding site in the atom. This principle was observed in the simulation. Based on table 1, when photon energy is greater than work function of the metal there is an ejection. There was a little exception on the sodium metal when it is flashed with a 695 nm of light source. The photon energy under this wavelength is 2.86 x 10 -19 J which is larger than the work function of sodium at 2.28 x 10 -19 J (Tipler & Llewellyn, 1999). The electron/s should have been ejected from the sodium metal surface but there was not. This was the limitation of the PhET simulations. There is no label on the simulation on what is the work function of each metal. This caused the no standardization of the value of the work function and it might be actually higher than 2.86 x 10 -19 J. Since there is no given standard, this study used the value presented by Tipler & Llewellyn (1999). The data from the photoelectron's kinetic energy and the light source frequency were plotted using MS Excel. The graph shown is a perfect straight line from both metals. The values were precise at R 2 = 1. The gradient of the graph is the Planck's constant and it showcased correctly the constant from the line equation. For sodium the graph presented the work function equal to 2.28 x 10 -19 J and for copper it is 4.7 x 10 -19 J. The perfectness of the graph is due to the fact the Planck's constant equal to 6.63 x 10 -34 J-s was utilized in computing the kinetic energy so the graph would really show a perfect straight line.

Photoelectrons Kinetic Energy against Light Frequency
Another improvement on the PhET simulation is that the simulation should include a section showing the kinetic energy of the emitted electrons. With this, the students can gather data from the kinetic energy of the photoelectrons and the frequency of light source is computed based from the wavelength. Then, students can verify the Planck's constant and perfect error analysis. Although, the graph of the photoelectron's kinetic energy and the light source frequency is found on the left corner of the simulation, this does not provide the value of the kinetic energy of the emitted electrons. One can say that there is an error to determine this kinetic energy and frequency and can lead to error on the graph. Further discussion on the next section.

The Relationship between Photoelectric Current and Light Intensity
The wavelength of the light source remained constant all throughout the experiment which was recorded as 339 nm under the ultraviolet spectra. The intensity of light source was varied from 14% to 83%. The data of the photoelectric current were taken from the simulation itself, located at the lower right corner. The data was plotted in MS Excel. The number of electrons released when a photoelectric effect occurs is directly related to the intensity of the incoming light. The more intense the light hitting the photosensitive surface becomes, the greater the number of electrons ejected as a result. This is due to the increase in incident photons and therefore an increase in photoelectric current. This is shown in equation 8. The graph in figure 3 shown exactly what the theory is. The gradient is 0.0034 s -1 . The R 2 of 0.9996 which shows precision and accuracy of the data. This is one of the best features of the PhET photoelectric effect simulation. The student can record the intensity and the current and draw a graph for themselves and measure the gradient. They can do this as well in MS Excel. This can allow bridging between theory and practice. Gal, et al (2020) argued that analyzing graphs is an important skill for students to develop since graphs are used in a variety of contexts, from the academic world to business and government. By examining a graph, Bowen & Roth (2015) explained that students can gain insight into the relationships between different variables, spot trends and outliers, and answer specific questions. Understanding how to read and interpret graphs is also important to being able to explain their meaning to others.

Analysis of Generated Graphs in PhET
There are three graphs generated in this PhET simulations. These are: current verses battery voltage, current versus light intensity, and electron energy and frequency. This analysis focused on the last two graphs. These graphs are located on the right corner of the screen. The user can click on the graph he/she wanted to generated and use for study. There is also a button where the user can increase and decrease the size of the graph. The user could also click on the camera for see the experimental parameters like the type of material, wavelength, intensity, and voltage. The camera and the size button are shown in figure 4 and figure 5. The graph, in figure 4 created by the PhET showed that photoelectric current and light intensity is directly proportional to each other as theory predicted and based from equation 8. However, in classroom practice it would be difficult for the student to compute the gradient of the graph since there is no data on the y and x axis. It would be a better improvement if the students can compute the gradient of the generated graph from PhET. They can compare their data from the PhET as the standard and they can compute the percent error. The graph on figure 5 revealed that there is a direct relationship between the photoelectron's kinetic energy and light frequency with respect on the metal sodium. This graph was similarly generated by this paper as shown in figure 2. The graph generated by PhET contain the title of the graph, the energy in electron volts, and the frequency of light. Notice that line of the graph is thick and this may present an error when a student attempt to measure the gradient of the graph. Weatherly (2023) argued that if a student tried to make the line unclear by drawing it with a thick pencil, it can cause error when trying to calculate the y-intercept from the graph.
The gradient of the graph in figure 5 is the Planck's constant, similarly in figure 2. To measure this gradient of figure 5, the change in the y-axis was divided to the change in the x axis as shown in figure 6. Using this process, the computed h was 6.47 x 10 -34 Js. The percent error of this graph would be 2.4%. This percent error was almost similar to the one gathered by Dasmo, et al y x (2019) at 0.15%. The error in graph is based on the thickness of the graph as mentioned by Weartherly (2023) plus the students need to estimate the upper value of y-axis and estimate its lower y value. The estimation can cause the error. It would be better if the line is thinner so the estimate is near to the correct value and this can reduce the error on the h.
Overall, the PhET simulations can be used to illustrate the photoelectric effect in a fun, interactive way. The simulations make it possible to explore and visualize the photoelectric effect with different types of light, such as radio waves, microwaves, and visible light. Users can adjust parameters like the intensity of the photon energy and observe how this affects the kinetic energy of electrons emitted. Lindgren, et al (2016) cited that this type of simulation, students are able to gain a more comprehensive understanding of how electrons interact with light. Additionally, student engagement increases when they are actively involved in exploring concepts through simulations rather than just reading a textbook or lecture.

CONCLUSIONS
The use of PhET simulations for investigating the photoelectric effect is a useful and engaging learning tool. Students can observe the effects in simulated form, allowing them to gain a deeper understanding of the complex physical processes at play. By using this simulation, students can see how changing various parameters affects the phenomenon, explore its underlying behavior and reach meaningful conclusions. Therefore, it is clear that using PhETs on photoelectric effect can be an effective educational tool in teaching this important physics concept.
Moreover, the simulation can also be improved if the work function of the metal is present on the simulation so that the students can clearly see the standard work functions. It can also be the kinetic energy of the photon electron is present. In this way, either the kinetic energy or the work function is to be computed and students can compare their answer to the standard value and measure the percent error. Additionally, the thickness of the line of the graph should be thinner to reduce the error on estimating. Another one is for the proper values of the y axis and the x axis on the current and intensity graph. It was difficult to measure the gradient of the y and x axis since there were no values.