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, the electron and the neutrino are emitted at right angles to each other. The electron ( mass 9.11×1031kg ) has a speed of 5.7×107 m/s and the neutrino has a momentum of 6.9×1024 kgm/s .

Part A

What is the recoil speed of the nucleus?

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, the electron and the neutrino are emitted at right angles to each other. The electron ( mass 9.11×1031kg ) has a speed of 5.7×107 m/s and the neutrino has a momentum of 6.9×1024 kgm/s .

Part A

What is the recoil speed of the nucleus?

Explanation / Answer

by conservation of momentum, the nucleus will have a recoil mom = resultant mom ot the emitted particles.
Momentum of electron (ignoring relativistic effects at v = 0.2c) ..
m v = (9.11 x 10-31 kg) x (5.7 x 107) m/s

= 5.1927 x10-23 kg.m/s
Resultant momentum (R) of particles (vectors combined by Pythagoras) ..

R² = (5.1927 x 10-23)2 + (6.9 x 10-24)
R = 5.819 x 10-23 kg.m/s

momentum of recoiling nucleus = M n x v = 5.819 x 10-23 kg.m/s  

v = (5.819 x 10-23 kg.m/s) / (2.34 x 10-26 kg

= 24868 m/s

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