Question

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How fast would two nuclei have to move so that in a head-on collision they would get close enough to fuse? (Treat the nuclei as point charges, and assume that a separation of 1.0 × 10-15 m is required for fusion.) Express your answer using two significant figures. Constants If two deuterium nuclei (charge +e, mass 3.34 x 10-27kg) get close enough together, the attraction of the strong nuclear force will fuse them to make an isotope of helium, releasing vast amounts of energy. The range of this force is about 10-15m. This is the principle behind the fusion reactor. The deuterium nuclei are moving much too fast to be contained by physical walls, so they are confined magnetically. m/s Submit Request Answer PartB What strength magnetic field is needed to make deuterium nuclei with this speed travel in a circle of diameter 3.00 m? Express your answer using two significant figures

Answer 1

Suppose speed of each nuclei = v K.E = 1/2 mv^2 + 1/2 mv^2 = mv^2 m = 3.34 times 10^-27 kg Finally potential energy = K q_1 q_2/r q_1 = q_2 = 1.6 times 10^-19 c r = 10^-15 m So initial K.E = final P.E so mv^2 = K q_1 q_2/r 3.34 times 10^-27 r^2 = 9 times 10^9 times (1.6 times 10^-19)^2/(10^-15) from here v = 8.3 times 10^6 ms^-1 radius = r = mv/Bq = d/2 r = 1.5m = 3.34 times 10^-27 times 8.3 times 10^6/B times 1.6 times 10^-19 B = 0.11558T