Teacher’s Guide Introduction to Quantum Mechanics Overview Students are introduced to the concept of electron waves and probability distributions. Students explore electron interference and diffraction and how electrons differ from particles when encountering barrier with slits in it. Students learn how the wave nature of an electron allows electrons to tunnel through barriers, how two nuclei can share an electron in a covalent bond, and how electron waves and energy levels in an atom are related. Learning Objectives Students will be able to: Define a probability distribution and explain how it relates to an electron wave Compare how particles interact with slits to how electrons interact with slits Describe how an electron can appear on the other side of a barrier Use the concept of electron waves to explain the sharing of electrons in a covalent bond Student Prerequisite Knowledge Students should already have a basic understanding of: probability atoms, ions, and chemical bonding quantized energy levels in an atom interference and diffraction as it relates to waves Background and resources http://www.colorado.edu/physics/2000/schroedinger/index.html - Experiments on Wave Interference http://www.chemistry.mcmaster.ca/esam/Chapter_3/section_2.html - More information about the probability density of an electron around a hydrogen atom Approximate time for lesson completion: 60 minutes Activity Answer Guide Page 1: Page 4: 1. Describe your designs of new dartboards 1. Based on your observations from the above simulations, which of the following must be true? that will result in the probability distribution patterns shown by the images to the left? One example might be to say that you get the most points for hitting the yellow triangles. This would cause the pattern to change in a way that would have more dots concentrated on the yellow areas and less on the red areas. 2. Give an example of probability distribution and describe how you may visualize it. You could record on a map where people have the flu and the areas with higher concentrations of dots indicate where you are more likely to catch the flu. Page 2: 1. The motion of the electron wave is most like: (b) A water ripple bouncing off a rock 2. Observe the two simulations above carefully. The motion of the ball and the motion of the electron wave have one thing in common. What is it? The motion is symmetrical about one axis. Page 3: 1. Based on your observation from the above simulations, which of the following must be true? (b) Electrons behave more like water waves in the single-slit experiments. 2. If you click one of the rectangular obstacles in the above quantum model and type DELETE to remove it, what will you observe when you run the simulation? Try to explain your observation using the concept of electron wave. The electron wave behaves like water waves bending around a barrier. (diffraction of waves) (b) Electrons behave more like water waves in the single-slit experiments. 2. If you click one of the rectangular barriers and resize it so that one of the slits is closed, what will you observe when you run the simulation? It will behave like the single slit experiment. You will stop the interference pattern and only see diffraction. Page 5: 1. Use the "Step through" button to run the tunneling model on the right step by step. Take a snapshot that shows the tunneling of the electron. 2. How does the snapshot you took in the window to the left show quantum tunneling of an electron? 3. Take a snapshot that shows the formation of a proton and a hydrogen anion and add some annotations to explain it. It shows how the chance of finding the electron occurs on both sides of the barrier. Page 6: 1.Why does the electron wave always tend to surround a proton? The electron wave represents the probable position of the electron. The electron has a negative charge, so it will be attracted to the positive charge of the nucleus. The electron wave shows the close proximity of the electron and the nucleus by surrounding the nucleus. 2. Take a snapshot that shows the formation of a hydrogen molecule and add some annotations to explain it. 4. Take a snapshot that shows the formation of two hydrogen atoms and add some annotations to explain it. Page 7: 1. Which of the following readings of the frequency slider did you find capable of exciting the electron? (b) 1 2. Describe how you determined the answer to the question to the left based on the observation from the above simulation. When I set the oscillation frequency to 1, I get a stable electron distribution with two peaks (at least temporarily), indicating the shape of the electron probability distribution is now in a “stable” excited state. 3. What frequencies other than the one you have selected for the above question can excite the electron? Explain your answer based on your observation. If you wait a long time at frequency 3 a new stable electron distribution occurs that shows four peaks. 4. What trend about the change of the shape of the electron wave did you observe when you moved the mouse from the lowest energy level to the highest one? Explain your observation. As the energy level increases, the number of peaks in the electron wave increases. A ball moves smoothly from on place to another in a straight line. An electron wave spreads out to describe the locations an electron is likely to be found. When a ball hits a wall it rebounds, but when an electron hits a barrier is causes the electron wave to “ripple” and sometimes the electron can tunnel through the wall. 4. The three images below show the motion of the electron wave in a container similar to what you saw on Page 2 but with a different condition. Explain what this sequence of images shows. This sequence of images shows an electron tunneling through the side of its container. 5. The pictures below are the results of two experiments. One shows the results of a machine gun shooting at a barrier with two slits the other an electron gun shooting at a barrier with two slits. In both images, a bright spot represents a hit. Can you tell which one is which? Explain your answer. The machine gun bullets will act like bouncy balls. The bullets will be found in two clusters, one behind each slit. Thus, the picture on the right represents the results of machine gun bullets hitting the barrier. The electrons will diffract and interfere as they pass through the slits, creating several regions where electrons will hit the screen. The picture on the left represents the results of electrons striking a barrier with two slits. Page 8 1. What phenomenon is shown in the image to the left? (b) Diffraction 2. Which of the following does an electron wave NOT represent? (d) The energy of an electron. 3. Describe the difference between the motion of a bouncy ball and the motion of an electron wave. 6. When a quantum leap happens to an electron in an atom, what has NOT changed? (b) The ground state. 7. When an electron wave becomes shared equally by two nuclei the result is (c) a covalent bond Further Extensions Discuss the Davisson-Germer experiment, which proved that electrons diffracted when they interact with crystals. Explore electron microscopy, which is used to view objects on the atomic scale using electrons and analyze the structure of materials using electron diffraction Discuss how electrons in a hydrogen atom can have different quantum numbers, and how those quantum numbers result in different probability distributions.