Lab 14 Phy 112 Turn in

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Katya Milyard PHY112 23138 6/9/23 Photoelectric Effect Lab Purpose/Question : The purpose of this lab is to explore the correlation and relationship between the frequency of the light used to free an electron from a metal source and the maximum kinetic energy of a free electron. Materials : ● Phet photoelectric effect simulation Procedures : 1. Download the Phet simulation for the photoelectric effect. 2. Play around with the brightness and wavelength lamp controls and observe the behavior of the freed electron a. The wavelength setting of the lamp controls that color of the light that is emitted from the lamp. In this particular simulation, the lamp can be set to emit specific wavelengths that are below and above the light range that is visible to the eye. b. The intensity setting of the lamp controls the brightness. This setting relates to the number of photons that are emitted by the lamp in the simulation. 3. Change the voltage setting and observe how the freed electrons behave. a. The voltage of the battery can be set to a positive potential on either plate in this simulation. 4. Put the lamp at a specific wavelength that causes an electron to become free and record the wavelength. 5. Figure out the voltage of the battery needed to drop the current to zero causing a stop in the potential. 6. Change the light wavelength and repeat the entire process until you collect a minimum of 10 data points. 7. Using the wavelength, calculate the frequencies for all the light photons. 8. Using the stopping potential, calculated the maximum kinetic energy of the electron that became free using the SI units for energy. 9. Make a graph in excel of frequency vs energy with frequency on the horizontal axis and energy on the vertical. Put in the line of best fit with the equation on the graph. Photograph(s) of Experiment :

Name: Katya Milyard Date: 6/10/23 Section: 23138 Data : Wavelength (lambda) Stopping Potential (volts) Frequency (Hertz) Maximum Kinetic Energy (Joules) 476 -.3 6.29 x 10^14 4.8x10 ^-20 404 -.9 7.42 x 10^14 1.44 x 10 ^ -19 448 -.5 6.69 x 10^14 8.0 x 10 ^ -20 390 -1.3 7.69 x 10^14 2.08 x 10 ^ -19 420 -.7 7.14 x 10^14 1.12 x 10^ -19 437 -.7 6.86 x 10^14 1.12 x 10^ -19

467 -.3 6.42 x 10^14 4.8x10 ^-20 489 -.3 6.13 x 10^14 4.8x10 ^-20 456 -.5 6.57 x 10^14 8.0 x 10 ^ -20 423 -.7 7.09 x 10^14 1.12 x 10^ -19 Calculations and Graphs : Calculations: Frequency calculation: c=(lambda)f Ex: 3x10^8= (476x10^-9)f f=6.3x10^14 Hz Maximum kinetic energy calculation: K=qV Ex: K=(1.6x10^-19)(.3V) K=4.8x10 ^-20 J Graphs: Results : This graph portrays a positive linear relationship between frequency and kinetic energy with a line of best fit equation of y = 1E-33x - 6E-19 and roughly a 92% correlation in this graph.

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Conclusion : ● Theory / Background : In this experiment, we are analyzing the photoelectric effect. In order to understand the photoelectric effect, we have to first understand a photon. A photon is a particle that acts like a massless particle with a specific amount of energy. The frequency of a light wave is directly proportional to the energy of a photon which creates the equation of E= hf where E is the energy of the photon, h is Planck’s constant that is equal to 6.63 x 10 ^ -34 m 2 kg/ s, and f is the frequency. This equation implies that photons with specific colors have the same constant energy due to the fact that they are the same color. For example, a photon of red light will have the same energy as another red photon while a blue photon will have a different constant energy compared to the red photon but the same energy as another blue photon. In this experiment, the light source could be adjusted to a variety of wavelengths. In this lab, the equation of c= (lambda)f was used to convert wavelength into frequencies. In this equation c is the speed of light that is 3 x 10 ^ 8 m/s, lambda is the wavelength in meters, and f is the frequency in Hz. In this experiment, we will learn that when photons from the lamp hit specific types of metals, the electrons that the metal can absorb the energy in order to move themselves to higher energy levels within the atom eventually making themselves free from the atom. When a photon has enough energy, the electrons can free itself from the atom. In this case, the minimum energy required to free an electron from the atom is a type of work function such as ionization energy. If the electron gives off more energy than is needed to free itself from the atom, it will use the leftover energy to move farther away from the metal. When the voltage of the battery is very large, the kinetic energy from the electrons that are freed will be converted into electric potential energy. In this case, the charge will not flow through the wires due to the fact that the current drops to zero. Stopping potential is the minimum amount of voltage required to convert maximum kinetic energy into electric potential. ● Interpretation of Results: In this lab, I was able to change the wavelength of the light source to determine the stopping potential at each wavelength. This information allowed me to calculate the maximum kinetic energy and frequency for each wavelength and create a graph of frequency versus kinetic energy with frequency in Hz on the x-axis and maximum kinetic energy in J on the y-axis. Based on the graph, we can see that there is a linear positive relationship between frequency and maximum kinetic energy with the line of best fit equation of y= 1E-33x-6E-19. Based on the graph, you can see a slight wave or polynomial shape that is consistent with the shape of a light wave. In the context of the graph, the x-axis intercept is the value of the cutoff frequency while the y-axis intercept is equal to the work function which is 6E-19. The slope of the graph is 1E-33; however, the slope of the graph is supposed to equal Planck’s constant, which is 6.63 E -34. This shows that the slope has a percent error of 50.82% through the calculation of (6.63E-34 - 1E-33)/ (6.63E-34) x 100 to

equal 50.82%. This percent error shows that there was a significant amount of error within the experiment. I was not expecting there to be this much error within the experiment. There could have been several sources of error. I could have possibly made some error in calculations, not using the simulation correctly, or possible rounding errors could significantly affect the data. My simulation also glitched a little bit that might have caused some error within the calculations and the data. Analysis Questions Response : Answer the following analysis questions: 1. Use the graph to determine the threshold frequency. Include the value, and explain how you determined the frequency. For this experiment the threshold frequency is equal to hf= ϕ . In order to calculate the threshold frequency, we need to first calculate ϕ . hf= ϕ + K (6.63x10^-34)(7.14x10^14)= ϕ + (1.12x10^-19) Φ = 3.61x10^-19 In this case the threshold frequency is (6.63x10^-34)f=3.61x10^-19 f=5.44x10 ^14 Hz 2. Use the graph to determine the work function for the metal. Include the value, and explain how you determined the work function. hf= ϕ + K (6.63x10^-34)(7.14x10^14)= ϕ + (1.12x10^-19) Φ = 3.61x10^-19 3. Explain how your results would change if you used a different light intensity value. If I used a different light intensity value, it would affect the stopping potential and the current which would directly affect the maximu m kinetic energy.

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