You are at the controls of a particle accelerator, sending a beam of 1.80 rimes

Question

You are at the controls of a particle accelerator, sending a beam of 1.80 rimes 10^7 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 1.50 times 10^7 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. Part B What is the speed of the unknown nucleus immediately after such a collision?

Explanation / Answer

from conservation of momentum

m1v1i = m1v1f + m1v2f

v1i + v1f = v2f

m2 = (m1v1i - m1v1f)/(v1i + v1f)

m2 = 1.67 x 10^-27 x 10^7 (1.8 - 1.5)/(1.8 + 1.5) x 10^7 = 1.52 x 10^-28

Hence, m2 = 1.52 x 10^-28 kg

b)v2f = v1i + v1f

v2f = (1.8 + 1.5)x 10^7 = 3.3 x 10^7 m/s

Hence, v2f = 3.3 x 10^7 m/s

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