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This is College Physics Answers with Shaun Dychko. And currently for the pwrite-up that is composed of 2 proloads with no electrons approximately them. So, fundamentally it"s the nucleus of a helium atom. And, it"s approaching a gold nucleus, which is composed of 79 protons, and also as it gets closer and closer, it is going to be decelerating and also getting sreduced and slower due to the repulsion from the gold nucleus. And, it"ll reach a final place, the distance R away from the nucleus such that its kinetic energy is lastly zero. And so, we"re given a kinetic energy that it starts via, and its last kinetic power will certainly be zero. And, we should number out the position R such that this last kinetic energy is zero. Now, the readjust in kinetic power is going to be the opposite to the change in its potential power, and also so it"s going to be getting potential energy as it gets closer and also closer to this nucleus. And, that"s going to be negative Q times the potential difference. So, the potential distinction through infinity being zero, is going to be K Q over R, and this capital Q is the charge in the gold nucleus, and also this lowerinstance Q right here is the charge of the alpha pwrite-up, which is two times the elementary charge, given that it is composed of 2 proloads. So, we"ll substitute K funding Q over R in area of V, and also we have actually the change in kinetic power then is negative little bit Q times K times capital Q split by R. And so, we"ll fix for R by mutiplying both sides by R over Delta KE. And, we gain this distance wbelow it"s cshed as it have the right to obtain to the nucleus. It"s going to be negative little Q K funding Q divided by the final kinetic power minus the initial kinetic power. Now, the last kinetic power is zero. And, now we plug in numbers. So, we have actually negative two times 1.6 times ten to the minus 19 Coulombs, this is the charge in the alpha pwrite-up, times Coulomb"s consistent times 79 times 1.6 times ten to the minus 19 Coulombs, which is the charge in the gold nucleus, separated by zero, final kinetic power, minus 5.00 times ten to the six electron volts converted into Joules by multiplying by 1.6 times ten to the minus 19 Joules per electron volts. And, we finish up through 4.55 times ten to the minus 14 meters is the closest these alpha particles deserve to obtain to gold nuclei.
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