I want to wrap up the unit on Electromagnetics, but feel as though one of the learning outcomes from our recent investigation was left unattended (see further thoughts in my reflection in this lesson). So, today, I return to the photoelectric effect in the hopes of attaining that learning outcome (NGSS Performance Expectation HS-PS4-3). The overall goal - a deep understanding of how the photoelectric effect demonstrates the particulate nature of light - is a very complex one and requires time. The first step, taken today, is to see that each metal requires a "threshold frequency" of incoming light - should the incoming light be below that threshold, no electrons will be liberated. This is what students could not see in the recent investigation and it is the purpose of today's work.
To begin the day, I present my students with a set of questions that are largely qualitative: familiarity with the relationships between frequency, wavelength, and energy can help address the first four questions without computation. The last question of the warmup, however, requires some computation. This exercise allows us to revisit NGSS Performance Expectation HS-PS4-1.
The questions are shown on the Smartboard and I encourage my students to consult their notes. Students may also work together and think the problems through with peers or with me. By wandering about, I can get a sense of the overall comfort with these recently explored topics.
After just about five minutes, I ask students to stop while I present the solutions. one at a time, and share some accompanying thoughts. In particular, I want to emphasize the idea that all electromagnetic waves travel at the same speed (the speed of light) and, therefore, questions 3 and 4 are "trick" questions.
We change gears to virtually explore the photoelectric effect. I provide my students a handout and take some time to review the controls of the simulation as well as explain the way in which we will collect data.
I call up the simulation and show the way in which one selects the input light for any given image. In addition, I show students how the battery is used to prevent liberated electrons from reaching across the gap between the plates. With a careful choice of battery voltage, one can get the electrons to stop just at the far plate - the condition at which the battery voltage is equal to the kinetic energy (in electron-volts) of the most energetic electrons. This stopping voltage is a critical measurement and changes with the input light frequency.
The student challenge is to select a variety of wavelengths and measure the resulting kinetic energy of the electrons using the process described above. To facilitate our exploration, I provide students with a spreadsheet which converts their wavelength choices into frequencies and their resulting kinetic energies can be entered. By the end of class, we are able to look at the assembled data and draw conclusions about the relationship between light and electrons. With this background, students begin to access the website and collect data.
Students access the website with their own devices or one of several that I have in the classroom. As they collect data, they come to the Smartboard and enter in the chosen wavelength and the measured stopping voltage. Many remark, tellingly, that the simulation is not working. When pressed for evidence, they say that "no electrons are flowing." This is a critical recognition - once they alter the wavelength to get electrons to flow there is a lingering impression that there are, indeed, limits to the photoelectric effect.
Here, students are engaging with the simulation.
In this image, these students show the limits of a four-person team for this activity. They combined forces when one computer failed to start properly; at least one student seems too far away from the computer to be truly engaged.
Near the end of the time allotted for this activity, we notice that there aren't many data points for Sodium. This student addresses this by re-entering the simulation to get a few more data points:
There is a flaw in this system: a logjam as students line up to enter data!
We continue in this mode until there are about ten minutes left in class. At that time, I get students to shift their attention from their computers to the Smartboard, where I display the assembled data and provide a quick analysis.
In the final few minutes of class, I ask students to shut down their computers and turn their attention to the Smartboard. There, I quickly make a scatter graph of the data we collected - frequency as the independent variable with electron kinetic energies, for a variety of metals, as the dependent variables.
First I show the graph of students' photoelectric data:
After appreciating the ideas that the data are quite linear and that best fit lines would likely have similar slopes, I enhance the graph with a line of best fit and calculate the slope:
Though my students are familiar with Planck's constant, they are used to seeing it in units of joules/Hertz. When I share the value in electron-volts/Hertz (4.1 x 10 -15), they are as impressed as I am with our result!
With this result, we arrive at a satisfying conclusion to the lesson. We can see that each metal has its own characteristic threshold frequency and that, once the photoelectric effect "turns on," the rate of change of the electron energy is always equal to Planck's constant. We can build upon these ideas in the next lesson.