The carbon isotope ^14C is used for carbon dating of areheological artifacts. ^1

Question

The carbon isotope ^14C is used for carbon dating of areheological artifacts. ^14C (mass 2.34 Times 10^-26 kg) 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 Times 10^-31 kg) has a speed of 4.5 Times 10^7 m/s and the neutrino has a momentum of 7.2 Times 10^-24 kg m/s. What is the recoil speed of the nucleus? Express your answer using two significant figures.

Explanation / Answer

Momentum = Mass x Velocity
Momentum of the Electron = (9.11*10^-31)(4.5*10^7) = 4.099 * 10^-23
Momentum of the Neutrino = 7.2*10^-24 Kg m/s

As the original momentum was zero (velocity was zero),
Initial Momentum = Final Momentum

Final_Momentum^2 = (7.2*10^-24)^2 + (4.099*10^-23)^2
Final_Momentum = 4.16 *10^-23
Speed = 4.16 *10^-23 / 2.34*10^-26
Speed = 1777.77 m/s

So the recoil speed of the nucleus = 1777.77 m/s

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