You are at the controls of a particle accelerator, sending a beam of 3.60×107 m/

Question

You are at the controls of a particle accelerator, sending a beam of 3.60×107 m/s protons (mass m ) at a gas target of an unknown element. Your detector tells you that some protons bounce straight back after a collision with one of the nuclei of the unknown element. All such protons rebound with a speed of 3.30×107 m/s . Assume that the initial speed of the target nucleus is negligible and the collision is elastic.Part A Find the mass of one nucleus of the unknown element. Express your answer in terms of the proton mass m . m Part B What is the speed of the unknown nucleus immediately after such a collision? m/s

Explanation / Answer

the mass of one nucleus of the unknown element is,

M = ([v10 - v1f]/ [v10 + v1f])m = [3.6x107 - (-3.3x107]/[3.6x107 + (-3.3x107])m = 23m

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vf = [2m1/m1 + m2] v10 = [2m/23m+m]v10 = [2/24]*3.6x107 = 3.00x106 m/s

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