How many electrons does it take to equal the mass of a proton?

Question

Accepted Answer

everyone in this example, we need to determine the number of electrons that have a total mass equal to that of two neutrons. So what we're going to want to do is recall that to find our number of electrons. We're going to take our two neutrons and multiply it by the mass of a neutron. And then we're going to be dividing this amount by our mass of our electron. And this quotation here is going to give us our number of electrons. So what we should also recall is that our mass of an electron is equal to 9.11 times 10 to the negative 31st power kilograms. And a mass of a neutron is equal to 1.675 times 10 to the negative 27 power kilograms. And so what we're going to get is that our number of electrons is equal to in our numerator. We're going to take the two neutrons and multiply it by the mass of those two neutrons equal to 1.675 times 10 to the negative 27th power kilograms. So that's the individual mass of the neutron. But we're gonna multiply it by two because we have two neutrons. And then in our denominator we're going to divide by the mass of an electron, which for a single electron is 9.11 times 10 to the negative 31st power kg. So what we're gonna do is in our numerator, we're going to have our product which is equal to 3.35 times 10 to the negative 27th power kilograms. And then in our denominator we're going to have our same value 9.11 times 10 to the negative 31st power kilograms. We can go ahead and cancel our units of kilograms because we just want the number of our electrons as our value. And so we're going to take the value of this quotient and our calculators. And this is going to give us our number of electrons equal to 3677 electrons. And so this is going to be the number of electrons to complete this example as our final answer. So I hope that everything be over viewed was clear. If you have any questions, please leave them down below and I will see everyone in the next practice video.

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