TAP 522-3: Rutherford scattering: directions of forces
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1 TP 522-3: Rutherford scattering: directions of forces Scattering of alpha particles Rutherford did not have a particle accelerator. Instead he used alpha particles, typically of energy 5 MeV, from radioactive decay. These questions are about the force of the on the alpha particle. n alpha particle has charge + 2 e, where e is the elementary unit of charge. has charge + Ze, where Z is the number of protons in the (and the number of electrons in the atom). Directions of forces Path of alpha particle scattered by The diagram shows an alpha particle approaching a massive from. ssume that the recoils negligibly as the alpha particle is scattered. 1. dd to the diagram an arrow showing the direction of the force on the alpha particle when it is at point, approaching the. Label the arrow F. 2. dd to the diagram an arrow showing the direction of the force on the alpha particle when it is at point, at its closest to the. Label the arrow F. 3. What is the ratio of the magnitudes of the two forces, F / F given the distances shown in the diagram? 4. dd to the diagram an arrow showing the direction of the force on the when the alpha particle is at point. Label the arrow F N. How does this force compare with the force F on the alpha particle at the same instant?
2 5. t which point,, or, is the alpha particle travelling slowest? 6. t which point,, or, is the alpha particle travelling fastest? 7. The does in fact recoil a little. dd an arrow labelled recoil to show the direction of recoil you expect as a result of the passage of an alpha particle along the whole path shown. Uphill downhill The electrical potential gradient around the can be thought of as like the slope of a hill. Imagine that you are riding on the alpha particle as it goes by the. re you riding uphill, downhill or momentarily along a contour of the hill: 8. t? 9. t? 10. t? 11. Is the electric potential at larger or smaller than the electric potential at? y what factor?
3 Practical advice These are intended as simple start-up questions for the discussion of alpha scattering. They are mainly qualitative, asking students to think about the direction of forces, and the nature of changes of kinetic and potential energy. The hill metaphor for potential is exploited. lternative approaches lpha particle orbits generated by a computer simulation could be studied is: Useful web site that includes a simulation of alpha particle scattering The following sections are relevant to this topic Plum pudding atoms, α scattering, Geiger & Marsden, Shells off tissue paper, Nucleus Social and human context The mathematical tools developed by the French mathematicians in the 1700s to deal with planetary orbits in the solar system were just as useful for alpha particle orbits under a repulsive force. nswers and worked solutions 1. The repulsive force is along the line joining the alpha particle and the. Path of alpha particle scattered by F 2. The repulsive force is along the line joining the alpha particle and the.
4 Path of alpha particle scattered by F F 3. The force at is four times as large as the force at, because the distance is halved and the force varies as 1/r The force on the is equal and opposite to the force on the alpha particle. ut because the is much more massive, it recoils only slightly. Path of alpha particle scattered by F F F N
5 5. Particle moves slowest at, because this is the distance of closest approach, the particle has been decelerating due to repulsive force. fter it accelerates away. 6. Here the particle is furthest from the, the alpha particle has been accelerated between and and is therefore going fastest at. 7. The alpha particle path is symmetrical about the line from the to. So the net change of momentum of the is along this direction. Path of alpha particle scattered by F F recoil 8. Uphill, because the particle is approaching the but being pushed away from it. 9. long contour, because the particle is travelling at right angles to the direction of the force on it. 10. Downhill, because the particle is travelling away from the and is being pushed away from it. 11. Potential at larger than potential at by a factor of 2, because the distance is halved and the potential varies as 1/r. External reference This activity is taken from dvancing Physics chapter 17, 80S
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