Enter the depth of the potential well (ε), the finite distance at which the inter-particle potential is zero (σ), and the distance between particles (r) into the calculator to determine the Lennard-Jones Potential (U).
Lennard-Jones Potential Formula
The following formula is used to calculate the Lennard-Jones Potential.
U(r) = 4ε[(σ/r)^{12} - (σ/r)^6]Variables:
- U(r) is the Lennard-Jones Potential (Joules)
- ε is the depth of the potential well (Joules)
- σ is the finite distance at which the inter-particle potential is zero (meters)
- r is the distance between particles (meters)
To calculate the Lennard-Jones Potential, use the formula to evaluate the potential energy between two non-bonded particles based on their distance apart.
What is Lennard-Jones Potential?
The Lennard-Jones Potential is a mathematical model that describes the interaction between a pair of neutral atoms or molecules. It is characterized by a potential well, representing the energy minimum where the particles are in a stable configuration, and a repulsive part that dominates at short distances due to the Pauli exclusion principle. This potential is widely used in molecular dynamics simulations and theoretical chemistry to predict and analyze the behavior of gases, liquids, and solid states of matter.
How to Calculate Lennard-Jones Potential?
The following steps outline how to calculate the Lennard-Jones Potential.
- First, determine the depth of the potential well (ε) in Joules.
- Next, determine the finite distance at which the inter-particle potential is zero (σ) in meters.
- Next, determine the distance between particles (r) in meters.
- Next, gather the formula from above = U(r) = 4ε[(σ/r)^12 – (σ/r)^6].
- Finally, calculate the Lennard-Jones Potential (U) in Joules.
- After inserting the variables and calculating the result, check your answer with the calculator above.
Example Problem :
Use the following variables as an example problem to test your knowledge.
Depth of the potential well (ε) = 1.65 x 10^-21 Joules
Finite distance at which the inter-particle potential is zero (σ) = 3.4 x 10^-10 meters
Distance between particles (r) = 5.5 x 10^-10 meters
