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, a carbon nucelus initially at rest emits the neutrino along the positive x-axis while the electron is emitted along the positive y-axis. The electron ( mass 9.11×1031kg ) has a speed of 1.5×107 m/sand the neutrino has a momentum of 6.4×1024 kgm/s . What is the recoil speed of the nucleus?

Explanation / Answer

given,

mass of electron = 9.11 × 10^31 kg

speed of electon = 1.5 × 10^7 m/s

neutrino has a momentum of = 6.4 × 10^24 kgm/s

total mass = 2.34 × 10^26 kg

by conservation of momentum

initial horizontal momentum = final horizontal momentum

2.34 × 10^26 x v = 9.11 × 10^31 × 1.5 × 10^7

vx = 583.97 m/s

initial vertical momentum = final vertical momentum

2.34 × 10^26 x vy = 6.4 × 10^24

vy = 273.50 m/s

resultant velocity = sqrt(vx2 + vy2) = 644.84 m/s

Please rate my answer if you find it helpful, good luck...

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.