Question

The carbon isotope 14C is used for carbon dating of archeological artifacts. 14C ( mass 2.34×10−26kg) 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 9.11×10−31kg ) has a speed of 5.7×107 m/s and the neutrino has a momentum of 6.9×10−24 kg⋅m/s .

Part A What is the recoil speed of the nucleus?

Answer 1

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