The carbon isotope 14C is used for carbon dating of archeological artifacts. 14C

Question

The carbon isotope 14C is used for carbon dating of archeological artifacts. 14C ( mass 2.34×1026kg) 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 9.11×1031kg ) has a speed of 5.7×107 m/s and the neutrino has a momentum of 6.9×1024 kgm/s .

Part A

What is the recoil speed of the nucleus?

********* 24868 m/s is not the correct answer

Explanation / Answer

here,

mass = 2.34 * 10^-26 Kg
mass of electron = 9.11*10631 kg
speed of electron = 5.7*10^7 m/s
momentum of neutrino = 6.9 * 10^-24 kg.m/s

as we know :

moemntum = mass * velocity

Mass of Electron = (9.11*10^31) * (5.7*10^7) = 5.1927*10^-23 kg.m/s

as they are moving at 90 degrees therefore

Pnet = sqrt(Pe^2 + Pn^2)
Pnet = sqrt((5.1927*10^-23)^2 +(6.9 * 10^-24)^2)
Pnet = 5.238 * 10^-23 kg.m/s

Speed of nucleus is :

Pnet = mass * velocity
v = Pnet/m
v = (5.238 * 10^-23) / (2.34 * 10^-26)
v = 2.24*10^3 m/s

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