lified version of a real situation that occurs in the center of our sun. A proto

Question

lified version of a real situation that occurs in the center of our sun. A proton of charge +e moves directly toward a stationary deuterium nucleus, also of charge +e. (We assume that the deuterium does not move.) a. Determine the speed that the proton must move toward the deuterium when far from it so that it is able to get within 1.0 × 10-15 m before stopping (At this distance, there is a good chance that the proton and deuterium will fuse to form a helium nucleus. The fusion releases considerable energy.) Simplify and diagram (construct a bar chart) Sketch and translate Sketch the initial and final problem states. Choose a system. Represent mathematically Solve and evaluate Use the bar chart to apply a generalized work-energy equation.

Explanation / Answer

When the proton and the deuterium are 1.0E-15 m apart the potential energy of the system of charges

U = ke2/r = 9.0E+9 * (1.6E-19)2/ 1.0E-15

                    = 23.04 E-14 J

When the proton is far of there is no influence of the elcric field and the potential energy of the system is 0.

Conserving the total energy of the system, the KE energy of the proton must be equal to the potential energy at closest approach.

0.5 mv2 = 23.04 E-14 J

       mass of proton m = 1.673 E-27 kg

velocity of Proton v = sqrt(2*23.04E-24/1.673E-27) = 1.659 E+7 m/s

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