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15_Chapter 19 HomeworkCH19 Magnetism

# 15_Chapter 19 HomeworkCH19 Magnetism - Magnetism 19.32...

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Magnetism 155 19.32 Since the centripetal acceleration is furnished by the magnetic force acting on the ions, 2 mv qvB r = or the radius of the path is mv r qB = . Thus, the distance between the impact points (that is, the difference in the diameters of the paths followed by the U and the isotopes) is 238 235 U ( ) ( ) ( ) ( ) ( ) ( ) 238 235 238 235 5 27 19 2 2 2 3.00 10 m s kg 238 u 235 u 1.66 10 u 1.60 10 C 0.600 T v d r r m m qB = = × = × × or 2 3.11 10 m 3.11 cm d = × = 19.33 In the perfectly elastic, head-on collision between the -particle α and the initially stationary proton, conservation of momentum requires that m v 0 m v m v α α α p p + = while conservation of kinetic energy also requires that ( ) or p p v v α α 0 0 v 0 v v v = − = + . Using the fact that 4 p m m α = ( ) and combining these equations gives ( ) ( ) 0 0 4 or p p p m v m v m v α α = 0 4 v + + 3 5 v v α = and ( ) 0 0 0 3 5 8 5 p v v v v = + = Thus, 0 3 3 5 3 5 5 8 8 p p v v v v = = = α After the collision, each particle follows a circular path in the horizontal plane with the
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