_PCS 224 - Lab 1

Faculty of Science Department of Physics Laboratory Report Cover Page Course Number PCS 224 Course Title Solid State Physics Semester/Year Fall 2022 Instructor Dr. Rebello TA Name Lab/Tutorial Report No. 1 Report Title The Photoelectric Effect Section No. 07 Group No. 103 Submission Date 10:45am Oct 5, 2022 Due Date October 5, 2022 2:00pm Student Name Student ID Signature* Andrew Gregorio ****04292 AG Omid Mazinani ****14393 OM (Note: remove the first 4 digits from your student ID) *By signing above you attest that you have contributed to this submission and confirm that all work you have contributed to this submission is your own work. Any suspicion of copying or plagiarism in this work will result in an investigation of Academic Misconduct and may result in a “0” on the work, an “F” in the course, or possibly more severe penalties, as well as a Disciplinary Notice on your academic record under the Student Code of Academic Conduct, which can be found online at: http://www.ryerson.ca/content/dam/senate/policies/pol60.pdf

Introduction In this experiment we are going to measure the stopping voltages of different colors and in addition, measure the stopping voltages of different brightnesses of the same color to see whether the stopping voltages will differ or not. The main goal of this experiment is to understand Einstein’s model of light and to see if the brightness of colors really have an effect on the energy of photons or is it just the wavelength and frequency that determine the photons energy. In other words, is it the color or the brightness that is important in Einstein's model of light. Theory This experiment focuses on the photoelectric effect, so we are going to use the equations that are related to the subject in order to assist us in the experiment. The main equation is where Ke is the kinetic energy of a photon and phi is the work function which is 𝐸 = 𝐾? + ɸ the minimum amount of energy that is required to release an electron from a metal. We are going to use this equation to derive other useful equations. We know that so we 𝐾? = Δ𝑉???? can rearrange our main equation to get . The energy of a photon is 𝐸 = Δ𝑉???? + ɸ 𝐸 = ℎ𝑐/𝜆 where h is planck's constant, c is the speed of the light, and lambda is the wavelength of the color. We can also write E as . Now that we have a couple of equations, we can 𝐸 = ℎ? rearrange them to get a very useful one that will help us significantly in this experiment. As we can see this equation has the form of y=mx+b, so in order to find Δ𝑉???? = ℎ𝑐/𝜆 − ɸ the remaining parts (h and phi) we could graph our data in the experiment to find the work function and planck's constant. Procedure 1. The mercury vapor light source was turned on and warmed up for 5 minutes. 2. The multimeter was turned on and the cables were plugged into the multimeter to measure voltage. The dial was adjusted to measure DC voltage. 3. The battery on the photodiode apparatus was checked by plugging the black cable into the ground terminal on the photodiode apparatus and plugging the red cable into the “+6V MIN” terminal on the photodiode apparatus. The multimeter read above 6.0V. Then the red cable was plugged into the “-6V MIN” terminal on the photodiode apparatus. The multimeter read below -6.0V. 4. The cables were plugged into the “OUTPUT” terminals on the photodiode apparatus using the same polarity as the multimeter. 5. A paper was held up in front of the lamp to determine the brighter side, measurements were taken from that side.. 6. The coupling bar was rotated and the photodiode apparatus was directly across from the lens/grating. The position of the lens/grating was adjusted so that the light is sharply focused. 7. The coupling bar was rotated so that one of the wavelengths entered directly on the opening into the photodiode apparatus.

Graph 2: Similarly to the first chart, this chart also displays how the stopping voltage is inversely proportional with the slope approximately equal to 1240 eV*nm. Top to bottom ( Dark violet, violet, blue, green, yellow) Wavelength (nm) Energy voltage(eV) Chart 1: The results of the first order refracted light and the energy in voltage associated with it. Top to bottom ( Dark violet, violet, blue, green, yellow) Wavelength (nm) Energy voltage(eV) Chart 2: The results of the second order refracted light and the energy in voltage associated with it. Sample Calculations: 𝐸 𝑘 = ℎ𝑐 λ − ϕ

→ average work function ϕ = (1. 2106 + 1. 516)/2 = 1. 3633 ?𝑉 sample calculation (Dark violet-second order) ℎ = (𝐸 𝑘 + ϕ) * (λ/𝑐) ℎ = (1. 695 + 1. 516) * ((365. 5)/(3 * 10 8 )) = 3. 91206833×10 −15 ?𝑉 * ? 𝑃??𝑐??? ????? = ((4. 1357 × 10 −15 − 3. 91206833×10 −15 )/4. 1357 × 10 −15 ) * 100 = 5. 4% First order Accepted slope = 1240 eV*nm Calculated slope = 1078.8 eV*nm 𝑃??𝑐??? ????? = ((1240 − 1078. 8)/1240) * 100 = 13% Second order Accepted slope= 1240 eV*nm Calculated slope= 1187.2 eV*nm ???𝑐??? ????? = ((1240 − 1187. 2)/1240) * 100 = 4. 26% Uncertainties: λ ± 30?? σ λ =± 0. 00273598( ( 30 365.5 ) 2 =± 0. 000224567442 ?? Energy (V) V ± 0. 002 σ ℎ =± 3. 91206833×10 −15 ( 0.004472135955 1.516 ) 2 + ( 0.004472135955 1.695 ) 2 + ( 30 365.5 ) 2 =± 3. 21473061×10 −16 Slope: σ ? =± 5 * (0. 000224567442) 2 σ ? =± 0. 000502148066?? −1 σ ? =± 5 * (0. 002) 2 σ ? =± 0. 004472135955𝑉 σ ?/? =± 1078. 8 ( 0.000502148066 0.00251074033 ) 2 + ( 0.004472135955 0.02236067977 ) 2 =± 305. 1307183 𝑉 * ?? Wrap up questions: Q1) The differences between the energy of the wavelengths from the first order of light compared to the second order were insignificant for the first three results and were significant for the last two wavelengths. This is due to the inaccuracy of determining where to take the measurement for the yellow and green wavelengths since they appeared with larger widths compared to the shorter wavelengths. Q2) So based on our measurements, we saw that the stopping voltages for bright and dim of the same color were not significantly different but instead quite similar and this exactly refers to Einstein’s model of light which states that the stopping voltages depend on the wavelength and frequency of the light, not their brightness. Q3) In order to find the minimum frequency and maximum wavelength of light needed to release an electron

The third source of error was trying to match the detector to the desired wavelength from the light source. If the detector was not at an orthogonal angle to the light source there would be many other wavelengths interacting with the detector at different angles. This could be adjusted in future experiments by obtaining the angles of the wavelengths from the light source and using a protractor to angle the detector to the correct location to capture the desired wavelength. References Professor Carina Rebello lecture notes ( photoelectric effect ) Lab manual #1