What is the separation of the protons from each other when they momentarily come to a stop?

Mikal - 2009-11-09 06:29:11 - Physics

Two protons that are very far apart are hurled straight at each other, each with an initial kinetic energy of 0.22 MeV, where 1 mega electron volt is equal to 1106 (1.610-19) joules. What is the separation of the protons from each other when they momentarily come to a stop?

Best Answer:

energy of system (initial) = after ======================= initial separation = infinite, elec PE =0 final separation = r , come to rest KE =0 ========================== rest mass energy (moc^2) will get cancelled out initial = final 0 + 2[moc^2 + KE] = +9*10^9 e^2/r + 2[moc^2 + 0] 2[KE] = +9*10^9 e^2/r r = +9*10^9 e^2/(2*KE) r =+9*10^9*[1.6*10^-19]^2/(2*0.22*10^6*1.6*10^-19) r =+3.27*10^-15 meter

Answer:

energy of system (initial) = after ======================= initial separation = infinite, elec PE =0 final separation = r , come to rest KE =0 ========================== rest mass energy (moc^2) will get cancelled out initial = final 0 + 2[moc^2 + KE] = +9*10^9 e^2/r + 2[moc^2 + 0] 2[KE] = +9*10^9 e^2/r r = +9*10^9 e^2/(2*KE) r =+9*10^9*[1.6*10^-19]^2/(2*0.22*10^6*1.6*10^-19) r =+3.27*10^-15 meter