In Example 29.2 it was assumed that the initially stationary gold nucleus would remain motionless during a head-on collision with an \(8.3 \mathrm{MeV}\) alpha particle. What is the actual recoil speed of the gold nucleus after that elastic collision? Assume that the mass of a gold nucleus is exactly 50 times the mass of an alpha particle.

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EXAMPLE 29.2 Going for the gold! An 8.3 MeV alpha particle is shot directly toward the nucleus of a gold atom (atomic number 79). What is the distance of closest approach of the alpha particle to the nucleus? PREPARE Energy is conserved in electric interactions. Assume that the gold nucleus, which is much more massive than the alpha particle, does not move. Also recall that the electric field and potential of a sphere of charge can be found by treating the total charge as a point charge. FIGURE 29.7 is a before-and-after visual overview; the "before" situation is when the alpha is very far from the gold nucleus, and the "after" situation is when the alpha is at its distance of closest approach to the nucleus. The motion is in and out along a straight line.