Lennard-Jones Potential: Equilibrium Distance and Dissociation Work

[postfan]

Homework Statement

The Lennard-Jones equation shown below gives the potential energy of two atoms when they are separated by a distance r.
U(r)=4 U_0 \left[\left(\frac{r_0}{r}\right)^{12}-\left(\frac{r_0}{r}\right)^6\right]

a)What is the distance between atoms at the condition of stable equilibrium? (Enter r sub 0 or U sub 0 by typing r_0 or U_0). If you choose to give an approximate answer, be sure to give your answer to at least 4 digits after the decimal.

b)What is the minimum work needed to completely dissociate the molecule by separating the atoms from each other if they are initially at equilibrium? (Enter r sub 0 or U sub 0 by typing r_0 or U_0)

Homework Equations

The Attempt at a Solution

Honestly this looks like Ancient Greek to me. I have no shadow of inking of an idea on how to even start on this problem. If someone could help me that would be awesome!

 

[voko]

Homework Statement

The Lennard-Jones equation shown below gives the potential energy of two atoms when they are separated by a distance r.
$U(r)=4 U_0 \left[\left(\frac{r_0}{r}\right)^{12}-\left(\frac{r_0}{r}\right)^6\right]$

a)What is the distance between atoms at the condition of stable equilibrium? (Enter r sub 0 or U sub 0 by typing r_0 or U_0). If you choose to give an approximate answer, be sure to give your answer to at least 4 digits after the decimal.

b)What is the minimum work needed to completely dissociate the molecule by separating the atoms from each other if they are initially at equilibrium? (Enter r sub 0 or U sub 0 by typing r_0 or U_0)

Homework Equations

The Attempt at a Solution

Honestly this looks like Ancient Greek to me. I have no shadow of inking of an idea on how to even start on this problem. If someone could help me that would be awesome!

What is the condition of stable equilibrium?

 

[postfan]

Where there are no forces acting on an object.

 

[voko]

Where there are no forces acting on an object.

You mean the net force is zero.

If the force is zero, what can be said about the potential energy? How are they related?

 

[postfan]

If the force is 0 then the potential energy is zero?

 

[voko]

If the force is 0 then the potential energy is zero?

Why would that happen?

Again, what is the relation between force and potential energy?

 

[postfan]

I don't know.

 

[voko]

I don't know.

What is the definition of "potential energy"?

Given potential energy, can you determine the force?

 

[postfan]

Potential energy is the energy of an object or a system due to the position of the body or the arrangement of the particles of the system.

No you can't determine the force from the potential energy.

 

[postfan]

Wait a minute : U(\vec{r}) = - \int_{\vec{r}_{ref}}^{\vec{r}}\vec{F}\cdot d\vec{r}

 

[voko]

You need a review on potential energy and force. You seem to remember something, which is good, but you do not seem to have a solid understanding of the relationship between force and potential energy.

 

[postfan]

Wait, F(x) = -\frac{dU}{dx}

 

[voko]

You might want to look at my questions in #4 again.

 

[postfan]

If the force is 0 then the potential energy is 0.

 

[voko]

If the force is 0 then the potential energy is 0.

Does this follow from #12?

 

[postfan]

I figured it out, the answer to the first part is r_0*2^(1/6) and the second part is u_0. Thanks for your help!