By scattering positively charged alpha particles off of atoms in gold foil, Ernest Lord

Chapter 14, Problem 14.4.18

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By scattering positively charged alpha particles off of atoms in gold foil, Ernest Lord Rutherford demonstrated that atoms contain a nucleus of concentrated charge. The scattered alpha particles followed hyperbolic trajectories, as shown in Figure 14.30, and Rutherford was able to measure the angle . However, the value of alone was not enough for Rutherford to determine whether the nuclear charge is negative or positive. A negatively charged nucleus would exert an attractive force on the alpha particles, and the positively charged nucleus would exert a repulsive force, but in either case, the trajectory would be a hyperbola specified by the angle . Note that in Figure 14.30, the incoming particle would pass through the origin if it were not scattered by the nucleus at (d, 0). (a) The hyperbola is x2/a2y2/b2 = 1. Find a formula for b in terms of a and . (b) It turns out that the charge in the nucleus is positive, and that the alpha particles undergo a repulsive force. What must be true about the parameter a?