2) One electron-volt, eV, is equivalent to 1.6*10^-19 Joules of energy. Ignoring

Question

2) One electron-volt, eV, is equivalent to 1.6*10^-19 Joules of energy. Ignoring gravity, if two, infinitely separated, protons (mass = 2*10^-27 kg) are shot directly toward one another, each with 1 TeV of kinetic energy (T = 10^12), how close together (what separation distance in meters) will they get, before the Coulomb force (proton charge = 1.6*10^-19 Coulombs) of repulsion stops their motion and then makes them infinitely separate again? (Hint: Use conservation of energy: as the protons approach each other, their kinetic energy is being converted into electrical potential energy, such that at their closest point of approach all of the initial kinetic energy will have been converted into electrical potential energy.)

Explanation / Answer

charge of proton q = 1.6*10^-19 C mass of protons m = 2*10^-27 kg kinetic energy of proton K = 1 TeV = 1* 10^12 eV = 1.6* 10^-7 J At their closest point of approach all of the initial kinetic energy will have been converted into electrical potential energy. So, kqq / r^ 2 = K+K = 2K = 3.2*10^-7 J where k = coulomb's constant = 8.99*10^9 Nm^ 2/C^ 2 from above r^2 = kqq / ( 3.2*10^-7 ) = 7.192*10^-22 closest separation r = 2.681*10^-11 m

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