HW14 - schneiter (tcs639) – HW14 – Ross – (89152) 1...

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Unformatted text preview: schneiter (tcs639) – HW14 – Ross – (89152) 1 This print-out should have 7 questions. Multiple-choice questions may continue on the next column or page – find all choices before answering. 001 10.0 points A uranium nucleus 238 U may stay in one piece for billions of years, but sooner or later it de- cays into an α particle of mass 6 . 64 × 10 − 27 kg and 234 Th nucleus of mass 3 . 88 × 10 − 25 kg, and the decay process itself is extremely fast (it takes about 10 − 20 s). Suppose the uranium nucleus was at rest just before the decay. If the α particle is emitted at a speed of 2 . 95 × 10 7 m / s, what would be the recoil speed of the thorium nucleus? Correct answer: 5 . 04845 × 10 5 m / s. Explanation: Let : v α = 2 . 95 × 10 7 m / s , M α = 6 . 64 × 10 − 27 kg , and M Th = 3 . 88 × 10 − 25 kg . Use momentum conservation: Before the de- cay, the Uranium nucleus had zero momentum (it was at rest), and hence the net momentum vector of the decay products should total to zero: vector P tot = M α vectorv α + M Th vectorv Th = 0 . This means that the Thorium nucleus recoils in the direction exactly opposite to that of the α particle with speed bardbl vectorv Th bardbl = bardbl vectorv α bardbl M α M Th = (2 . 95 × 10 7 m / s) (6 . 64 × 10 − 27 kg) 3 . 88 × 10 − 25 kg = 5 . 04845 × 10 5 m / s ....
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This note was uploaded on 04/23/2009 for the course PHYS 152 taught by Professor Button during the Spring '08 term at IUPUI.

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HW14 - schneiter (tcs639) – HW14 – Ross – (89152) 1...

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