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

Question

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

Part B
What is the speed of the unknown nucleus immediately after such a collision?

please work through this in detail! I need to understand how! Thanks

Explanation / Answer

From conservation of momentum we have 1.67x10^-27*3.60x10^7 = -1.67x10^-27*3.30x10^7 + M*V So M*V = 1.67x10^-27*(3.60x10^7 + 3.30x10^7) = 1.152x10^-19kg-m/s From conservation of K we have 1/2*m*v1^2 =1/2*m*v2^2 + 1/2*M*V^2 So 1/2*1.67x10^-27*(3.60x10^7)^2 - 1/2*1.67x10^-27*(3.30x10^7)^2 = 1/2*M*V^2 so 1/2*M*V^2 = 1.728x10^-13 But M*V = 1.152X10^-19 so 1/2*1.152x10^-19*V = 1.728x10^-13 So V = 2*1.728x10^-13/1.152x10^-19 = 3.00x10^6m/s Therefore M = 1.152x10^-19/3.00x10^6 = 3.84x10^-26kg = 3.84x10^-26/1.67x10^-27kg/proton = 23 protons and again V = 3.0x10^6m/s

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