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 4.5×107 m/s and the neutrino has a momentum of 7.8×1024 kgm/s .

What is the recoil speed of the nucleus?

At what standard angle will the nucleus recoil?

Explanation / Answer

here,

mass of the nucleus , mn = 2.34 *10^-26 kg

mass of electron , me = 9.1 * 10^-31 kg

speed of electron , ve = 4.5 * 10^7 m/s

momentum of nutrino be Pn = 7.8 * 10^-24 kg.m/s

let the recoil speed of the nucleus be v and angle be theta

using conservation of momentum

mn*v*cos(theta) + Pn = 0

2.34 *10^-26 * v * cos(theta) = - 7.8 * 10^-24 .....(1)

using conservation of momentum along positive y axis

mn * v*sin(theta) + me*ve = 0

2.34 *10^-26 * v*sin(theta) = - 9.1 * 10^-31 *4.5 * 10^7....(2)

frrom equation (1) and (2)

theta = 79.22 degree

v = 1782.17 m/s

the recoil speed of the nucleus is 1782.17 m/s

the standard angle will the nucleus recoil with is 259.22 degree counter clockwise from the + x axis

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

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