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A mechatronics demonstration project called Quantum Leap, funded by the National Science Foundation. The project aims to help teachers illustrate key concepts in modern physics, such as the Bohr model of the atom, quantization of energy, and atomic spectra. The project uses a hands-on mechatronic device that allows students to test their predictions for energy and frequency values and observe emission and absorption spectra.
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The National Science Foundation^1
North Rockland High School Thiells, NY 10984
Middle College High School Long Island City, NY 11101 (^1) This work was supported by the National Science Foundation under a RET Site Grant 0227479.
The National Science Foundation^2 Abstract Concepts in modern physics are challenging to teach because students have to grasp models of microscopic and invisible particles. This project offers a visual demonstration of several key ideas in modern physics: the Bohr model of the atom; quantization of energy in photons; atomic spectra and the relationship between energy and frequency of light. “Quantum Leap” calls for students’ active participation with a hands-on approach. Hands-on activities are supported by contemporary literature examining the most effective ways to engage students in science. Quantum Leap allows students to test their predictions for values of energy and frequency and for emission and absorption spectra through a hands-on mechatronic device.
The National Science Foundation^4
This project addresses concepts in modern physics and quantum theory. It can be used to illustrate the Bohr model of the atom and the concept of quantized energy, and provides a visual representation of absorption and emission spectra. It correlates to the following New York State Physical Setting/Physics and Core Curriculum Standards: STANDARD 1—Analysis, Inquiry, and Design. Mathematical Analysis Students will use mathematical analysis, scientific inquiry, and engineering design, as appropriate, to pose questions, seek answers, and develop solutions. STANDARD 6—Interconnectedness: Common Themes Students will understand the relationships and common themes that connect mathematics, science, and technology and apply the themes to these and other areas of learning. STANDARD 7—Interdisciplinary Problem Solving Students will apply the knowledge and thinking skills of mathematics, science, and technology to address real-life problems and make informed decisions. STANDARD 4—The Physical Setting Students will understand and apply scientific concepts, principles, and theories pertaining to the physical setting and living environment and recognize the historical development of ideas in science. In particular, Quantum Leap addresses the following key ideas from Standard 4: Key Idea 4 - Energy exists in many forms, and when these forms change energy is conserved. Students will: 4.1 Observe and describe transmission of various forms of energy. 4.3 Explain variations in wavelength and frequency in terms of the source of the vibrations that produce them, e.g., molecules, electrons, and nuclear particles. Key Idea 5 - Energy and matter interact through forces that result in changes in motion. Students will: 5.3: Compare energy relationships within an atom's nucleus to those outside the nucleus 5.3i – interpret energy level diagrams 5.3ii – correlate spectral lines with an energy-level diagram The experiment also addresses the following performance indicators: Performance Indicators: 5.3a States of matter and energy are restricted to discrete values (quantized). 5.3c On the atomic level, energy is emitted or absorbed in discrete packets called photons. 5.3d The energy of a photon is proportional to its frequency.
The National Science Foundation^5 5.3e On the atomic level, energy and matter exhibit the characteristics of both waves and particles. 5.3f Among other things, mass-energy and charge are conserved at all levels (from subnuclear to cosmic). The project also supports the following National Education Technology Standards (NETS) as outlined by the International Society for Technology Education (ISTE): Standard Area 3: TEACHING, LEARNING, AND THE CURRICULUM. Teachers implement curriculum plans that include methods and strategies for applying technology to maximize student learning. Teachers will: A. Facilitate technology-enhanced experiences that address content standards and student technology standards. B. Use technology to support learner-centered strategies that address the diverse needs of students. C. Apply technology to develop students' higher order skills and creativity. D. Manage student-learning activities in a technology-enhanced environment.
You are probably reading this paper in a library or a classroom, and if you take a look up, chances are that you will see a fluorescent light. Have you ever wondered how fluorescent lights work? Did you know that there is no filament running through the long bulb, and it is filled only with gas? The Bohr model of the atom provides an explanation to this mystery, as well as to a range of other phenomena, from black light posters to lasers. Bohr’s model provides an atomic explanation to the concept that all forms of energy are packaged in discrete amounts - called quanta. This idea paved the road to the exciting field of quantum mechanics. 1 It also reaffirmed Einstein’s theory that light itself is made of tiny bundles of energy, and these bundles – or quanta
The National Science Foundation^7 3.1.B. The Bohr Model of the Atom Roughly two years after Rutherford’s experiment, Neils Bohr offered an explanation to rectify Rutherford’s model. Bohr proposed a model of the atom that allowed electrons to maintain specific energies and still orbit the atom. Bohr studied the hydrogen atom to develop his theory because it has the lowest atomic mass and the simplest bright-line spectrum. Bohr’s model explained the particular emission of colors from excited hydrogen atoms and why the electron does not collide with the nucleus. Bohr’s proposal was surprising and revolutionary. He suggested that electrons do not radiate energy even though they are accelerating as they change direction around the nucleus. He hypothesized that electrons orbiting an atom maintain the same energy within a given “energy level.” Each energy level has a fixed radius and may only be reached by emitting or absorbing a discrete amount of energy. The lowest energy level is closest to the nucleus and is called the ground state. Electrons occupying energy levels above the ground state are considered to be in an excited state. These energy levels proposed by Bohr came to be known as the Bohr model of the atom and showed distinct energies allowable for the hydrogen atom. (See figure 1.) Figure 1.^5
The National Science Foundation^8 3.1.C. Quantization of Energy When Bohr was trying to use Rutherford’s findings to determine a better model of the atom’s structure, he looked towards Einstein’s theory of light. Einstein’s proposed theory explained light was made up of discrete packets of energy that had the ability to act like particles. He called these packets of energy “photons.” This was a revolutionary idea not yet widely supported, but it worked very well with Bohr’s ideas. Bohr said that since light from atoms only was emitted at certain frequencies corresponding to certain colors, that light must relate to certain energies as described by Einstein’s theory: E = hf where E is the energy of the photon emitted or absorbed, h is Planck’s constant and f is the frequency of the light. The energy emitted or absorbed when an atomic electron changes energies is equal to the energy of a photon that can be calculated by finding the difference between energy levels: Ephoton = Einitial – Efinal where Einitial is the original energy level and Efinal is the energy level after the electron jump. These energies emitted or absorbed when an electron changes levels correspond to the light given off or absorbed when an electron jumps down or up a level, respectively. 6 3.1.D. Absorption and Emission Spectra A phenomenon long recognized by scientists was the emission and absorption of light by gaseous elements. The heated gas of an element will emit a color or colors characteristic of that element resulting in bright colored lines when viewed through a spectroscope. Similarly, cool gas will absorb certain colors from white light that is incident upon it which results in dark lines in the continuous spectrum when observed through a spectroscope. Figure 2. 7 Examples of emission and absorption spectra The Bohr model of the atom explains these phenomena through the quantization of energy. The photons emitted from the heated – excited – gaseous atoms correspond to certain colors and the
The National Science Foundation^10 yet display fundamentals of the Bohr model and absorption and emission spectra. Quantum Leap allows students to move an “electron;” see the color of light that would be emitted or absorbed; and note the amount of energy change that occurs.
4.1 Equipment List The list below covers the materials used to build the entire project, including mechanical, electrical and non-electrical components. The following sections will describe the major components in greater detail. Board of Education project board from Parallax Inc. Basic Stamp 2 Integrated Circuit from Parallax Inc. 7 Photoresistors Servo Motor 7 Resistors for LEDs 7 Resistors for photoresistors 2 Fiber Optic lighting 2 plates of 3/8” Plexiglass squares, 16” x 16” 2 3/8” Plexiglass squares, 8” x 8” 6 1” standoffs 16 1” long screws 2 ½” metal balls 2 bread boards 7 LEDs (Red, Yellow, Green, Red-Super Bright, Blue, UV) 4.2 Board of Education with Basic Stamp 2 The BASIC Stamp 2 (BS2) module is a very popular integrated circuit for learning purposes. This module normally has 2K bytes of program space and 16 Input/Output pins. It can be programmed to perform different and various applications with a simple, user-friendly programming language which is called “PBasic.” The BS2 is designed for Serial PC interface and also provides enhanced debug features, which make the learning process more efficient. The BS2 is mounted on the Board of Education (BOE) to constitute the microcontroller for this project. A microcontroller is basically a mini-computer (but without human interface such as keyboard and mouse) with a small amount of memory that can hold and execute PBasic programs. The BOE also serves as a breadboard for circuitry and comes with a DB9 connector
The National Science Foundation^11 for (serial) communication with the BS2. The BOE provides power to the project – it is driven by a 6-14V direct current (VDC), while an integrated voltage regulator provides a steady %VDC output to the BS2 integrated circuit. Figure 3 below shows the BOE and BS2: (a) (b) (c) Figure 3: Board of Education (a), Board of Education schematic (b), and Basic Stamp 2 (c). 9 4.3 Photoresistors A photoresistor is a variable resistor that changes its value according to the intensity of light. Under dark conditions, its resistance would be very high (ideally, in the absence of light conductivity should be zero but practically the resistance is about few mega-ohms), but when exposed to light its resistance would drop to a very low value (in the range of few hundred ohms). Photoresistors are usually made of cadmium sulfide and are very sensitive to light, and thus can be used to detect lighting conditions. When the lighting conditions change, the voltage across the resistor changes and the current flowing through the resistor changes. 10 Figure 4 shows 2 common photoresistors (a) and the common schematic representation (b). The light arrow indicates a variable resistance, and the dark arrow indicates that the incident light triggers the change in the resistance: (a) (b) Figure 4: Photoresistors (a), and Schematic of photoresistor (b).
The National Science Foundation^13 (a) (b) Figure 6: Transistor (a), and Schematic of Transistor (b). 4.6 Servo Motor A motor is a mechanism that converts electrical energy to mechanical energy (a generator does the reverse process, i.e. converts mechanical into electrical energy). A servo motor has various advantages over a regular motor. The major characteristics of a servo motor are speed and direction control. By enhancing a regular motor with a gearbox, potentiometer, control circuitry and a control input, the microcontroller can send different commands to the motor and change its speed and direction according to desired conditions set by the user. In this project, the servo motor is calibrated to move a needle to point to specific energy level on an energy scale. This action is achieved by the BS2 sending the signal with the PULSOUT command. This command can control the angle of rotation of the servomotor. (a) (b) Figure 7: Servomotor (a), and Schematic of Servomotor (b).
Quantum Leap was created to allow a student to freely choose which energy level transition an electron in a hydrogen atom will make (based on the Bohr model of the atom) or to illustrate a
The National Science Foundation^14 transition as specified by a given physics problem. The student or teacher will move a small metal sphere that represents the electron by using a clear wand to the initial energy level and then to a different level or to a point representing ionization of the electron. The levels and ionization point are represented by holes drilled into the user interface where the metal ball will easily sit. Once an initial level is chosen and the ball has been placed there for a moment, the user may then move the ball to the next desired position. Once this transition is made, a light display will show either the color of light emitted or the spectrum with the absorbed color missing. At the same time, the servomotor will move a needle that will point to the corresponding energy change of this jump and frequency range. At this time, the user may chose to reset the Quantum Leap or make a second energy level transition.
Quantum Leap is powered by an AC outlet through a DC adapter, which is connected to the BoE. Photoresistors detect the placement of the “electron” by the user. Once the initial and final placements of the electron are detected by the photoresistors, the program running inside BS processes these values at the pins connected to the photoresistors as either high or low. The program then sets the appropriate pins controlling the LEDs high or low, which then light the fiber optics. At this time, the program also directs the servomotor how much to turn in order to land the needle upon the proper energy and frequency values. (See Figure 7.)
The National Science Foundation^16 by the photoresistor, current flows and the pin turns low. Conversely, when there is no light reaching the resistor, the resistance gets infinitely high and no current flows to the pin, creating a potential difference, and turning the pin high. The LEDs are each connected to Vdd and then to an appropriate resistor, which protects both the pin of the microcontroller and the LED from receiving too much current. Resistors used vary based on the specifications of each LED. The LED and resistor are connected to the collector pin of an NPN-transistor. The base of the transistor is connected to a pin of the microcontroller and the emitter pin of the transistor is connected to ground. This transistor acts as a switch. When the pin is turned low, a potential difference is detected and current flows through the transistor turning on the LED. When the pin is set low, the LED remains dark. To offer further protection to the delicate pin of the microcontroller, a 470 Ω resistor is placed between it and the base pin of the transistor. (See figure 9.)
The National Science Foundation^17 Figure 9 SHEET (^) 1 OF 1 Vdd
... Vdd Vdd Vdd P (^7) P^8 P 1 3 P 12 P 0 P 1 P 2 P 3 P 4 P 5 Vdd Vdd Vdd Vdd Vdd Vdd Servomotor (^39) 0 (^) P 3 Vd d Amanda Gunning Ram Avni SMART 2004
P 6 Vdd
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Quantum Leap successfully shows one or several consecutive electron energy level transitions when used properly with the plexiglass wand. False readings are often generated when a user uses his or her hand to move the metal ball because photoresistors are unintentionally triggered from the hand’s shadow. Also, if one leans over the device or passes one’s hand over the photoresistors it is possible to mistakenly trigger the photoresistor. This glitch was addressed by creating the wand for moving the electron, which is effective in limiting this problem, and by putting the heat-shrink tubing around each photoresistor, which also helps. Overall, Quantum Leap is deemed successful by its developers.
The goal of the authors of the developers of Quantum Leap was to create a device that could successfully model bright-line emission and absorption spectra in an engaging way for students. Students will be able to first calculate on their own: the expected energy gain or loss by the electron; frequency of the emitted or absorbed photon; and based on the New York State Board of Regents Reference Table, the color of the light of that frequency. Students may then check their answers using Quantum Leap. Of course, students and teachers may also simply move the electron to different energy states and observe the results. Based on its operational success and the positive reactions from other science teachers and professionals in the field of science and education, the developers of Quantum Leap believe the device will successfully engage students in the classroom and demonstrate concepts in modern physics.
A. Enhance the “Quantum Leap” so that a user can enter the initial and final energy levels in a computer or other user interface, and the device will move the electron automatically. B. Write a computer program that takes a specific color as input, and shows the motion of the electron as output. C. Write a computer program that displays the emission and absorption spectra on the computer screen in addition to the LED display.
The National Science Foundation^20
The following activities are suggested in order to gain students’ conceptual understanding before drilling into mathematical calculations and Regents review questions. These activities can be modified by teachers as they find fit, integrate them into existing lesson plans, or add them as extension. In the following questions, students should refer to the Bohr Model of the hydrogen atom: 9.2.A. Fill in the blanks: The Bohr model of the hydrogen atom supports the idea that all forms of _______ are quantized. A quantum is a _______ amount. According to Einstein, light itself is made of tiny bundles of energy, and these bundles – or quanta – are known as _______. The most stable condition of an electron is called the _______ state. In order to move outwards, away from the nucleus, an electron has to _______ energy. Each energy level above the ground state is called an _______ state, because the electron had to be “shaken up” in order to leave its most cozy, stable state. Therefore, when an electron moves to a higher energy level (further from the ground state), we would expect to see an _______ spectra. In typical absorption spectra, all the frequencies, or colors, would be _______, and only one frequency or color would be _______. Ground Absorption Fixed Photons Missing Energy Absorb Excited Present 9.2.B. Answer the Following Questions The following questions can be used as activities for both small groups and individual work. Each group may use the “quantum Leap” project to test their predictions or to visualize a given situation:
