Energy of the Nucleus. How much work is needed to assemble an atomic nucleus containing three pr

step 1 So the three protons form an equilateral triangle. So I'm going to go ahead and draw a little di

Energy of the Nucleus. How much work is needed to assemble...

Key Concepts

Coulomb's Law

Coulomb's Law describes the force between two point charges, stating that the force is directly proportional to the product of the charges and inversely proportional to the square of the distance between them. This law is foundational for calculating interactions between charged particles and is used to derive the potential energy between any two charges.

Electrostatic Potential Energy

Electrostatic potential energy is the energy stored in a system of charged particles due to their positions relative to each other. In the context of assembling a nucleus or any arrangement of charges, it represents the work required to bring the charges from infinity to their specific configuration, overcoming the repulsive or attractive forces as described by Coulomb's law.

Superposition of Pairwise Interactions

The principle of superposition allows the total potential energy of a system of multiple charges to be calculated as the sum of the potential energies of each pair of charges. This concept is essential in calculating the overall work needed to assemble a system like an atomic nucleus from individual charged particles.

Transcript

00:01 So the three protons form an equilateral triangle.

00:04 So i'm going to go ahead and draw a little diagram to help us better understand this problem.

00:09 So these dots actually represent the protons, and hold on, let me draw a third one.

00:15 And as you can see, these three protons have formed an equilateral triangle.

00:19 Let me just draw the radiuses between the two to help you better understand.

00:24 So i call this distance r.

00:27 And since it's an equilateral triangle, the radius is the same for all of them.

00:32 So let me just label the charges q1, q1, q1, 2, q3.

00:37 Q1, q2, q3.

00:41 All right.

00:42 So now we know the radius is equal to 2 times 10 to the, hold on, let me rewrite that.

00:52 You know that the radius which is given to us is 2 times 10 to the negative 15 meters.

01:02 All right, so obviously this is a very small distance, but it's also important to note that the distance between all the three charges are equal to the radius and are constant for all of them.

01:15 So now to find the total amount, now to find the amount of work for one done by one charge, we know the, we know the equation is the amount of work is equal to cool constant times charge one, charge two over the radius, separating them.

01:42 This is the work done between the two charges.

01:45 So if you have three charges, there is a total of three different exertions of force.

01:53 So we must add the total weight, i mean the total work done.

01:57 So if you were to add the total work done, and since the charges are the same, the radius are the same, we can just multiply this value by a constant of three.

02:10 And again, since the charges are the same, we can just make.

02:14 Make it q squared, since charge one and charge two are the same thing.

02:22 Q squared times three, these are brackets, over the, hold on, the radius is also included in the brackets.

02:35 Oh, here, let me get theories going.

02:40 Let me just start over, right.

02:42 So, three times coolant constant times the two charges, q squared, over the radius.

02:55 So this is the total breakdown.

03:00 And now if you're just plug in the constants that we have, so coolum's constant, as you all know is 8 .99 times 10 to the power of 9 metam squared over the column squared for the units.

03:15 So 3 times 8 .99 times 10 to the power of 9...

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