Part A and Part B Problem 9.71 - MC Part A The carbon isotope 4C is used for car

Question

Part A and Part B

Problem 9.71 - MC Part A The carbon isotope 4C is used for carbon dating of archeological artifacts. 14C (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 r-axis while the electron is emitted along the positive y-axis The electron (mass 9.11 x 10 31 kg) has a speed of 1.8 107 m/s and the neutrino has a momentum of 6.3x10-24 kg- m/s What is the recoil speed of the nucleus? Express your answer using three significant figures Hints Hint 1. Total Momentum (click to open) Hint 2. Components 1 (click to open) Hint 3. Components 2 (click to open) u= 1850 m/s Submit My Answers Give Up Incorrect, Iry Again Part B At what standard angle will the nucleus recoil? Express your answer using three significant figures

Explanation / Answer

Momentum = Mass x Velocity

Momentum of the Electron = (9.11x10^-31)(1.8x10^7) = 1.64x10^-23

Momentum of the Neutrino = 6.3x10^-24

As the original momentum was zero (velocity was zero so the mass times 0 = 0), then the momenta must equal each other. As the electron and the neutrino were at 90* to each other you can draw a triangle and use pythagoras' theorem to calculate the recoil momentum, and from that the speed.

A^2 = B^2 + C^2

Momentum^2 = (6.3x10^-24)^2 + (1.64x10^-23)^2

Momentum = 1.757x10^-23

Speed = momentum/mass = 1.757x10^-23 / 2.34x10^-26

Speed = 751m/s

So the recoil speed of the nucleus is 751m/s

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