You are at the controls of a particle accelerator, sending a beam of 2.10×10 7 m

Question

You are at the controls of a particle accelerator, sending a beam of 2.10×107 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 1.80×107 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 .

Part B

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

Explanation / Answer

let the mass of one nuclei be M and velocity be v m/s

initial momentum

m*2.1*10^7

final momentum

m*1.8*10^7 +M*V

conserving momentum

Mv=0.3m*10^7 ...........(i)

now conserving velocity

0.5*m*(2.1*10^7)^2=0.5*m*(1.8*10^7)^2+0.5Mv^2

Mv^2=1.17m*10^14..............(ii)

solving (i) and (ii)

Part B ->v=39000000 m/s

part A -> mass =M=0.0769 kg

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