he carbon isotope 14C is used for carbon dating of objects. A 14C nucleus can ch

Question

he 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 7.0x10-24 kg-m/s. If the electron and anti neutrino are emitted at right angles from each other, calculate the recoil speed of the nucleus.

Explanation / Answer

Applying momentum conservation,

pi = pf

0 = (9.11 x 10^-31)(4 x 10^7)i + (7 x 10^-24)j + p_n

|p_n| = sqrt(36.4^2 + 7^2) x 10^-24 = 37.1 x 10^-24kg m/s

speed = Pn / m = (37.1 x 10^-24) / (2.34 x 10^-26)

v = 1584 m/s

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