homework help Problem 9.71 - MC Part A The carbon isotope 14C is used for carbon

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Problem 9.71 - MC Part A The carbon isotope 14C is used for carbon dating of archeological artifacts. 1C (mass 2.34 × 10-26 kg) decays by the process known as beta decay in which the nucleus emits an electron (the beta particle) and a subatomic particle called a neutrino. In one such decay, a carbon nucelus initially at rest emits the neutrino along the positive -axis while the electron is emitted along the positive y-axis. The electron (mass 9.11 × 10-31 kg ) has a speed of 1 .6×107 m/s and the neutrino has a momentum of 7.2x10-24 kg - m/s What is the recoil speed of the nucleus? Express your answer using three significant figures Hints u= m/s Submit My Answers Give Up Part B At what standard angle will the nucleus recoil? Express your answer using three significant figures Hints from the positive -axis Submit My Answers Give Up Provide Feedback Continue

Explanation / Answer

Applying momentum conservation,

0 = (9.11 x 10^-31)(1.6 x 10^7)j + (7.2 x 10^-24)j + (2.34 x 10^-26) v

v = - 622.9j - 307.7i

(A) Speed = sqrt(622.9^2 + 307.7^2) = 695 m/s

(B) angle = 180 + tan^-1(622.9/307.7) =244 deg

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