1) The nucleus of an atom consists of protons and neutrons (no electrons). A nuc

Question

1) The nucleus of an atom consists of protons and neutrons (no electrons). A nucleus of a carbon-12 isotope contains six protons and six neutrons, while a nitrogen-14 nucleus comprises seven protons and seven neutrons. You perform a nuclear physics experiment in which you bombard nitrogen-14 nuclei with very high speed carbon-12 nuclei emerging from a particle accelerator. As a result of each such collision, the two nuclei disintegrate completely and a mix of different particles are emitted, including electrons, protons, antiprotons (with electric charge –e each), positrons (with charge e each), and various neutral particles (including neutrons and neutrinos). For a particular collision you detect the emitted products and find 17 protons, 4 antiprotons, 7 positrons, and 27 neutral particles. How many electrons are also emitted?

2) Two new particles, which have identical positive charge q3, are placed the same 0.0734 meters apart, and the force between them is measured to be the same as that between the original particles. What is q3?

Two new particles, which have identical positive charge q3, are placed the same 0.0734 meters apart, and the force between them is measured to be the same as that between the original particles. What is q3?

Explanation / Answer

1) The collision will preserve several quantities: net charge, net baryon number, and net lepton number, along with energy, momentum, etc. The conservation of net charge is the only relevant quantity to figuring out this particular problem.

The total charge before hand is 7+6 = 13. We see that in this event the outgoing protons (+17) and antiprotons (-4) already equate to 13. So the remaining particles (the positrons, electrons, and neutrals) must add up to zero.

So the answer is that 6 electrons must be produced to balance the remaining charge.

2)

F = ke(q3q3)/r² = ke(q3)²/r²
Fr² = ke(q3)²
Fr²/ke = (q3)²
(q3)² = Fr²/ke
q3 = (Fr²/ke)

q3 = (F (0.0734 m)²/8.987552 x 10^9 Nm²/C²)
WE dont know F

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