Evaluating the location r_m of the minimum of potential

[tasleem moossun]

Homework Statement

A gas of neutral atoms is often modeled as an ideal gas, where the gas atoms are considered to be "elastic billiard balls" that only interact by bouncing off each other in a manner that conservers the total kinetic energy.

Homework Equations

V(r) = 4(Epsilon)[(delta/r)^12 - (delta/r)^6]

in dimensionless form
U(xi) = 4 [(1/xi)^12 - (1/xi)^6]

xi= delta/r, U = V(r)/epsilon

The Attempt at a Solution

so i differentiated V(r) to get F(r),since F(r) = - dV(r)/dr.The force at the minimum of the potential is zero and the potential minimum defines the equilibrium position of the system.

 

[DrClaude]

Do you have a question?

Generally speaking, you can find the extrema (minimum, maximum, saddle point) of any function f(x) by calculating when its derivative is 0. You don't need to invoke the force here.

 

[tasleem moossun]

my question was how do i evaluate the location of r_m of the minimum potential.

 

[mfb]

Like this:

The force at the minimum of the potential is zero and the potential minimum defines the equilibrium position of the system.

 

[tasleem moossun]

so basically the location of r_m would be -4(epsilon)[(-12(delta^12)/r^13 + 6delta^6/r^7]

 

[mfb]

No, it is the r where this expression is zero.