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/sand the neutrino has a momentum of 7.3×1024 kgm/s .

What is the recoil speed of the nucleus?

The answer is not 1900 or 1600 m/s...

Explanation / Answer

given,

mass of electron = 9.11 × 10^31 kg

speed of electon = 5.7 × 10^7 m/s

neutrino has a momentum of = 7.3 × 10^24 kgm/s

total mass = 2.34 × 10^26kg

by conservation of momentum

initial horizontal momentum = final horizontal momentum

2.34 × 10^26 * v_x = 9.11 × 10^31 × 5.7 × 10^7

v_x = 2219.1 m/s

initial vertical momentum = final vertical momentum

2.34 × 10^26 * v_y = 7.3 × 10^24

v_x = 311.966 m/s

resultant velocity = sqrt(2219.1^2 + 311.966^2

resultant velocity = 2240.921 m/s

recoil speed of the nucleus = 2240.921 m/s

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