Exploration: Rutherford s Scattering Explanation The purpose of this exploration is to become familiar with Rutherford s analysis that formed a crucial part of his idea of a nuclear atom. To assist you as you work through this exercise, click on the toolbox to the right to open the Scattering applet. If you need help understanding the simulation and variables, see the Help menu for assistance. The Simulation Model This simulation shows only the near-the-nucleus approach of the incident alpha particle and is based on the assumption that the majority of atom is empty space in which the electrons are believed to exist. 1. Suggest some reasons why the electrons can be ignored in this scattering experiment. 2. What is the range of impact parameters available in this simulation? 3. How does this compare with the size of a gold nucleus? Use the scale ruler to measure the gold nucleus. 4. How does the maximum range of impact parameters compare with the size of a gold atom (radius 135 pm)? Click Auto fire. Let the simulation run until the scattering pattern is clear. 5. State the characteristics of the scattering pattern that agree with the evidence from Rutherford s experiment. 1
6. What evidence is not shown in this model? Force and Distance 7. What type of force acts between the alpha particle and the nucleus? Set the alpha particle energy at 15 MeV. Make sure that Random alpha particle position is not checked and the impact parameter is set to 0.0 fm. Click the Fire button. 8. Where along the path of the alpha particle is the electric force at its maximum value? 9. Use the Scale ruler to measure the distance between the centres of the alpha particle and the gold nucleus when the force is at its maximum. 10. Calculate the force at this distance and draw a diagram labeled with force arrows. 11. Predict the change in the magnitude of the electric force from the starting position of the alpha particle until it has rebounded completely back. Describe in words and include a sketch of a force versus distance graph (no numbers required). 12. Check your prediction by selecting Show Graph in the Options menu. If you are asked to produce a graph for a report, select the Table icon in the title bar of the graph display. Click the copy data icon, paste the evidence into a spreadsheet program and generate a graph of electric force versus distance. 2
13. Set the impact parameter to 5.0 fm and fire the alpha particle. Sketch the result and draw vector arrows to label the direction of the electric force at three positions of the alpha particle approaching at about five nuclear radii, at the closest approach and recoiling at about five nuclear radii. The calculation of force at various distances in #13 requires a two-dimensional vector analysis. Rutherford and his associates were able to do these tedious force calculations manually without the help of computers (as in this simulation). 14. How would your sketch in #13 change if the nuclear charge were much smaller? Check your prediction using aluminium as the element. 15. Suggest a method that Rutherford may have used to estimate the nuclear charge. Rutherford initially estimated the nuclear charge to be approximately ½ Ae (where A is the atomic mass). 16. Evaluate his prediction for the different elements in this simulation. While Rutherford was continuing to do additional experiments, other scientists were starting to investigate the suggestion by van den Broek (in 1913) that the nuclear charge may be the same magnitude as the atomic number. Rutherford was aware of this and used the developing information to revise his own work. 3
Energy Factors Rutherford had some control over the kinetic energy of the alpha particles; however, he expressed regret that he could not obtain alpha particles with as high an energy as he wanted to use. 17. Using the range of energy available and a random alpha particle position checked, compare the scattering patterns of low, medium and high energy alpha particles. Describe this in words or sketches (you could run several different simulations simultaneously in separate windows). 18. How does your answer to the previous question suggest an approximate method of determining the nuclear size? 19. For a particular approach (such as an impact parameter of 0.0 fm) and recoil of an alpha particle, predict qualitatively the changes in kinetic energy, potential energy and total energy. 20. Run a simulation for a single alpha particle and check your prediction by selecting Show Graph in the Options menu. If you are asked to produce a graph for a report, select the Table icon in the title bar of the graph display. Click the copy data icon, paste the evidence into a spreadsheet program and generate a graph of energy versus distance showing three lines corresponding to E k, E p, and E total. 21. Using the law of conservation of mechanical energy, show that the minimum distance, r, can be calculated using the equation: r = kq 1q 2. Verify the units on both sides of this max E k equation. 4
22. Use the equation in the previous question to calculate the minimum distance for a 15 MeV alpha particle. Compare your answer to #9 above and evaluate. 23. Run some simulations using the maximum energy of alpha particle, 0 fm for the impact parameter and four different elements. What surprising result did you obtain in these simulations (similar results also obtained by Rutherford)? What should be done next? Evaluation of Rutherford s Nuclear Hypothesis Scientific theories and other theoretical knowledge must satisfy a number of criteria (see CRYSTAL-AB site). Explaining the known evidence is easier than predicting the results of future experiments. A theory can always be adjusted to fit the known evidence, but predicting future results is a difficult test. Once Rutherford had the idea of a nucleus from the results of early experiments, he did some detailed mathematical analyses to predict what factors should affect the scattering pattern. He predicted that the number of scattered particles should be proportional to the thickness of the foil and the square of the nuclear charge, and inversely proportional to the fourth power of the velocity. These specific predictions were subsequently tested and verified by Geiger and Marsden in a series of experiments. The description of Rutherford s work given above is an excellent example of a common type of scientific reasoning known as hypothetico-deductive reasoning (see CRYSTAL-AB site). In this type of reasoning a hypothesis based on previous evidence is used to make a specific prediction that is then tested in an experiment, and finally the experimental result is compared with the prediction. The hypothesis is either verified or falsified based on the agreement between the predicted outcome and experimental result. 5