what is the recoil speed of the nucleus?at what standard angle in the nucleus re

Question

what is the recoil speed of the nucleus?at what standard angle in the nucleus recoils?

MasteringPhysics | https://session.masteringphysics.com/myct/itemView?assig Homework #8 Problem 9.71-Mc Part A y M Problem 9.71 - MC The carbon isotope 1C 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 arn 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 z-axis while the electron is emitted along the positive y-axis. The electron ( mass 9.11 × 10 31 kg ) has a speed of 1.4x107 m/s and the neutrino has a momentum of 7.8x10-24 kg m/s Ex rias) Part B Exp

Explanation / Answer

Applying momentum conservation,

0 = (9.11 x 10^-31)(1.4 x 10^7)j + (7.8 x 10^-24)i + (2.34 x 10^-26) v

v = - 333.33 i - 545 j m/s

Speed = sqrt( 333.33^2 + 545^2 )

= 639 m/s .........Ans

angle = tan^-1(545/333.3) = 58.5 deg

from +ve x axis = 180 + 58.5 = 238.5 counterclockwise

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