The carbon isotope 14C is used for carbon dating of archeological artifacts. 14C

Question

The carbon isotope 14C is used for carbon dating of archeological artifacts. 14C ( mass 2.34×1026kg) 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 x-axis while the electron is emitted along the positive y-axis. The electron ( mass 9.11×1031kg ) has a speed of 2.0×107 m/s and the neutrino has a momentum of 8.2×1024 kgm/s . What is the recoil speed of the nucleus? At what standard angle will the nucleus recoil?

Explanation / Answer

Please find the solution in below picture

given,

mass of electron = 9.11 × 10^31 kg

speed of electon = 2 × 10^7 m/s

neutrino has a momentum of = 8.2 × 10^24 kgm/s

total mass = 2.34 × 10^26kg

by conservation of momentum

initial horizontal momentum = final horizontal momentum

2.34 × 10^26 * v_x = 9.11 × 10^31 × 2 × 10^7

v_x = 778.63 m/s

initial vertical momentum = final vertical momentum

2.34 × 10^26 * v_y = 8.2 × 10^24

v_x = 350.43 m/s

resultant velocity = sqrt(v_x2 + v_y2)

recoil speed of the nucleus = 853.85 m/s

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