The carbon isotope C is used for carbon dating of objects. A 14C nucleus can cha

Question

The carbon isotope C 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 x10^7 m/s. While the anti-neutrino has a momentum of 8.5x10^-24-m/s. If the electron and anti-neutrino are emitted at right angles from each other, calculate the recoil speed of the nucleus.

Explanation / Answer

momentum of caRBON AFTER emitting electron is Sqrt[(8.5*10^-24)^2 + (9.11*10^-31*4*10^7)^2] = 37.4*10^-24 = 2.34*10^-26*v

v = 1599 m/s

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