Question

The carbon isotope 14C is used for carbon dating of objects. A 14C nucleus can change into a different kind of element, a neighbor on the periodic table with lower mass, by emitting a beta particle – an electron or positron – plus a neutrino or an anti-neutrino. Consider the scenario where 14C ( mass of 2.34 x 10 -26) decays by emitting an electron and anti neutrino. The electron has a mass of 9.11x 10-31 kg and a speed of 4.0 x107 m/s. While the anti neutrino has a momentum of 2.5x10-24 kg-m/s. If the electron and anti neutrino are emitted at right angles from each other, calculate the recoil speed of the nucleus.

Answer 1

Momentum of system during decay of 14C, remains conserved. Assuming14C to be at rest before decay, initial momentum is zero. Hence sum of momentums of electron, anti-neutrino and 14C after decay is zero. Hence