Solving the Van der Waals Force Problem - Talib

In summary, the conversation is about the Lennard-Jones potential and its mathematical description of the interaction between particles. The conversation includes discussions on sketching the potential, identifying forbidden regions, estimating the number of allowed energy levels, and calculating the energies of these levels. The conversation also mentions the use of the potential in solid-state and quantum studies.
  • #1
Talib
7
0
Hello,

Can anyone lead me or give me a hint on how to solve this problem?

Interaction between neutral atoms and molecules can be decomposed to
two different forces: an attractive force at large distances (the Van der
Waals force), and a repulsive force at short distances (due to overlap between electron wavefunctions). A simple mathematical description of this
interaction between two particles is given by the Lennard-Jones potential:


U (r) = 4*epsilon [(sigma/r)^12 - (sigma/r)^6]


where [sigma] and [epsilon] are empirical parameters (epsilon is the depth of the potential well and sigma is the (finite) distance at which the potential is zero), and r is the distance between the particles.

(a) Sketch this potential.

(b) Are there any forbidden regions? If so, what are they and why? If
not, why not?

(c) Obtain an estimate for the number of allowed energy levels corresponding
to bounded states.

(d) Calculate the energies of these (bounded) energy levels.

Thanks a lot! :D

Talib
 
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  • #2
Talib said:
Hello,

Can anyone lead me or give me a hint on how to solve this problem?

Interaction between neutral atoms and molecules can be decomposed to
two different forces: an attractive force at large distances (the Van der
Waals force), and a repulsive force at short distances (due to overlap between electron wavefunctions). A simple mathematical description of this
interaction between two particles is given by the Lennard-Jones potential:


U (r) = 4*epsilon [(sigma/r)^12 - (sigma/r)^6]


where [sigma] and [epsilon] are empirical parameters (epsilon is the depth of the potential well and sigma is the (finite) distance at which the potential is zero), and r is the distance between the particles.

(a) Sketch this potential.

(b) Are there any forbidden regions? If so, what are they and why? If
not, why not?

(c) Obtain an estimate for the number of allowed energy levels corresponding
to bounded states.

(d) Calculate the energies of these (bounded) energy levels.

Thanks a lot! :D

Talib

have you even tried yet?

I'll get you started on a). You're basically just looking at U as a function of r, everything else is a constant. plot the points r at 0 and r at infnite to get a couple ideas for how the graph looks. You can also take the derivative and set it to 0 to find minimums and maximums.
 
  • #3
aite thanks .. i figured the drawing .. but how can i obtain an estimate of the # of allowed energy levels??
 
  • #4
Talib said:
aite thanks .. i figured the drawing .. but how can i obtain an estimate of the # of allowed energy levels??

I'm taking solid-state right now, I haven't done quantum yet, so that's where I saw Leonard-Jones potentials, and we just solved for minimum energy.

I'm thinking it will have to do with your minimums on your graph, since minimums in potential energy usually represent a stable equilibrium.
 

FAQ: Solving the Van der Waals Force Problem - Talib

What is the Van der Waals force problem?

The Van der Waals force problem refers to the challenge of accurately modeling and predicting the interactions between molecules in close proximity. These forces, also known as London dispersion forces, are weak intermolecular forces that are responsible for various phenomena such as surface tension, solubility, and the stability of molecular structures.

Why is solving the Van der Waals force problem important?

Solving the Van der Waals force problem is crucial for understanding the behavior of molecules and materials at a microscopic level. It has applications in fields such as chemistry, physics, and materials science, and can lead to advancements in areas like drug design, nanotechnology, and energy storage.

What approaches are being used to solve the Van der Waals force problem?

Scientists are using a combination of experimental techniques, computer simulations, and theoretical models to tackle the Van der Waals force problem. Some approaches include density functional theory, molecular dynamics simulations, and quantum mechanical calculations.

What are the current limitations in solving the Van der Waals force problem?

One of the main limitations in solving the Van der Waals force problem is the complexity of the interactions involved. The forces are highly dependent on the geometry and composition of the molecules, making it challenging to develop a universal model. Additionally, the accuracy of current methods is limited by computational power and the approximations used in calculations.

What advancements have been made in solving the Van der Waals force problem?

Recent advancements in computer technology have allowed for more accurate and efficient simulations of Van der Waals forces. Additionally, the development of new theoretical models and experimental techniques has provided deeper insights into the nature of these forces. However, the problem is still not fully solved, and further research is needed to improve our understanding and predictive capabilities.

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