Magnetism15519.32Since the centripetal acceleration is furnished by the magnetic force acting on the ions, 2mvqvBr=or the radius of the path is mvrqB=. Thus, the distance between the impact points (that is, the difference in the diameters of the paths followed by the Uand the isotopes) is 238235U()()()()()()23823523823552719222 3.0010 m skg238 u235 u1.6610u1.6010C0.600 TvdrrmmqB−−∆=−=−×=−××or 23.1110m3.11 cmd−∆=×=19.33In the perfectly elastic, head-on collision between the -particleαand the initially stationary proton, conservation of momentum requires that m v0m vm vαααpp+=while conservation of kinetic energy also requires that ()or ppvvαα00v0vvv−= −−=+. Using the fact that 4pmmα=()and combining these equations gives ()()004orpppmvmvmvαα=04v++35vvα=and ()0003585pvvvv=+=Thus, 033535588ppvvvv===αAfter the collision, each particle follows a circular path in the horizontal plane with the
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