According to Coulomb's law, which pair of charged particles has the lowest potential energy? a. a particle with a 1- charge separated by 150 pm from a particle with a 2+ charge b. a particle with a 1- charge separated by 150 pm from a particle with a 1+ charge c. a particle with a 1- charge separated by 100 pm from a particle with a 3+ charge

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Hey everyone and welcome back to another video according to Koms Law, which pair of charged particles has the lowest potential energy. We have three answer choices A B and C. We're given two particles with different charges and separated by different distances. Now, what we're going to do in this problem is just recall the Cool Arms Law and specifically its version for the potential energy, the potential energy is equal to the Boltzmann's constant K multiplied by the magnitude of the first charge, the magnitude of the second charge and divided by the distance between them or basically the separation. So we don't really need to worry about the unit conversion or anything because we're just comparing three options with the same units. So let's go ahead and calculate the energies. So starting with E A, that's for part A, we can leave Boltzmann's constant sk because it doesn't really matter, right? We're just trying to rank them and we're going to use our first charge, it's negative one, the second charge is positive two, the separation between them is 150 Peters. So we don't need to worry about the units. Once again, we can just evaluate this result and we simply end up with negative 0.0133 K, right? That's our Boltzmann's constant and we can just proceed the same way. For part B, we're going to use K, we're going to use our charge of negative one and positive one because that's what we are given, right? And we're going to divide that by the separation of 150 Peters. So in this case, we get a result of negative 0.00667 K. And finally, for part C, we're going to use our K value, our charges in this case would be negative one and positive three. We're going to divide that by the separation of 100 Peters. And here we get a result of negative 0.03 00. OK. Right. So now we have our answers. We simply want to tell which one of these would give us the lowest potential energy. And what we noticed is that all of them are negative. The lowest number is the number with the highest magnitude if we exclude the sign. So that would be option C negative 0.03 is the lowest number of all of these. Notice how we don't really need to use the K value because we're only comparing at their relative magnitude right to each other. So we can essentially state that option C would be the correct option. A particle with a negative one charged separated by 100 peters from a particle with a three positive charge. That will be our final answer. And thank you for watching.

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Key Concepts

Coulomb's Law

Potential Energy of Charged Particles

Comparison of Charge Magnitudes