SCATTERING WHAT IS IT? ----------- This project models the scattering of particles from a target that repels them. An example of this is the scattering of alpha particles (helium nuclei) from a heavy nucleus such as gold. This experiment, first done by Rutherford, provided important evidence that the positive charge in an atom is concentrated in a small place. See the note below by Martin Rocek, a contributor to this model. The target nucleus is an immovable patch with a variable charge in the center of the screen. The size of the nucleus -- the radius of the ball of charge -- is also variable. A parallel beam of particles is sent upward from the bottom of the screen, and the path of each particle is traced. Each particle is repelled from the nucleus according to Coulomb's inverse square law, modified for a distributed nuclear charge. The particles do not interact with each other. HOW TO USE IT ------------- First select the number of particles with the NUMBER slider. Set their initial velocity with the VELOCITY slider. Set the charge of the target nucleus with the CHARGE slider. Set the radius of the charged nucleus with the RCORE slider. If RCORE is large, the charge is more spread out, but the amount of charge is the same. Then press the SETUP button. When the sliders have been set to desireable levels, press the GO button to begin the simulation. The SHOW-TARGET switch shows or hides the nucleus. The TRACE-MODE switch, when set to 1, has each turtle mark out its position every time-tick. Thus you can see the arcs formed by different particles' travels. The TRACE-MODE can be turned on and off while the model is running. The speed, position, and direction of one particle (who = 0) are displayed. The SCATTERDIS slider sets the starting x-coordinate of that specific particle. If SCATTERDIS is 0, the particle approaches the nucleus head-on. The SCATTERDIR monitor shows the particle's heading (zero is straight up). After the particle goes by the nucleus, this heading is the scattering angle . When TRACE-MODE is off, only that particle's path is shown. The speed and distance from the nucleus are plotted in the plotwindows. THINGS TO NOTICE ---------------- Each setting gives a family of paths for particles of constant velocity but different paths. What is the shape of each trajectory? Is it the same shape approaching and leaving the nucleus? What is the shape of the family of curves? How "big" does the target appear to be from the particles' point of view? What information does the scattering pattern give about the size of the nucleus? A very large nucleus represents J.J.Thompson's "plum pudding" model of the atom, in which the charge was thought to be spread out in a volume as large as the atom itself. A very small nucleus represents Rutherford's discovery, namely that the charge is concentrated in a very small nucleus, about 1/10000 the size of the atom. What about the size of the nuclear charge and the initial velocity? Martin Rocek, who made important modifications to this model, writes, "the main point of my modifications was introducing rcore; it has the effect of smoothing out the target, that is, making something more like the old "plum-pudding" model of the atom that held sway before Rutherford's experiment. When rcore is large enough, even though the scattering of particles with impact parameters significantly bigger than rcore is essentially unchanged, no particles experience large deflections. As you make rcore smaller, the hard core is restored, and large angle scattering returns." THINGS TO TRY ------------- You can study the trajectory of one particle by turning off TRACE-MODE. Change the SCATTERDIS slider to change how closely the particle passes by the nucleus. What happens to the particle's path when its velocity and the charge of the nucleus are changed? What needs to be true for particles to bounce almost straight backward? The value of the SCATTERDIR monitor, averaged over millions of particles, along with the particles' speed and the charge on the nucleus, is what an experimenter would actually be able to measure. Devise an experiment that would give information about the size of the nucleus from this information alone. If you knew the particle velocity and nuclear charge from other experiments, could you devise an experiment, using this model, that would determine the size of the nucleus? EXTENDING THE MODEL ------------------- Put in a different function for the force between the nucleus and the particles -- 1/r dependence, r dependence, attraction instead of repulsion. This can be done in the code preceeded by ;;force function in "move-turtles". A repulsive force will "scatter" the particles, but an attractive force will put some of them into orbits. Let the particles begin with a constant velocity, or give them all a random velocity. Or try giving each particle a variable charge, which directly affects the strength of the acting force upon it. Try having a lattice of nuclei, and vary their spacing. STARLOGOT FEATURES ----------------- When a particle moves off of the edge of the screen, StarlogoT keeps track of its virtual position even though it's not visible. Notice that all of the code within the procedure 'move-particles' is kept to turtle instructions. Almost all the variables are turtle-variables, even the position of the acting charge. Although it seems like it would make more sense to keep that value as a global variable, it is actually faster for StarLogoT to keep it inside each turtle. 'Turtle code' runs the fastest when kept free of outside distractions (such as the calling of an observer procedure). Even just one line of code could cause a significant slowdown. In fact, such a slowdown occurs already due to the presence of the code in 'go' that handles the clicking of the mouse button. This little bit of checking cuts the speed of "Gravitation" (another similar model) by about half. When you examine the procedure window, take note that the standard turtle primitives 'seth', 'fd 1', etc... aren't used here. Everything is done directly to the x-coordinates and y-coordinates of the turtles. RELATED MODELS -------------- "Gravitation" also calculates an inverse-square force between particles and changes their motion accordingly. In "Gravitation", each particle looks at EVERY OTHER particle, whereas in "Scattering", each particle interacts only with the nucleus.