# Evaluating the location r_m of the minimum of potential

1. Nov 3, 2015

### tasleem moossun

1. The problem statement, all variables and given/known data
A gas of neutral atoms is often modelled 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.

2. Relevant 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

3. 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.

2. Nov 3, 2015

### Staff: Mentor

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.

3. Nov 3, 2015

### tasleem moossun

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

4. Nov 3, 2015

Like this:

5. Nov 3, 2015

### tasleem moossun

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

6. Nov 3, 2015

### Staff: Mentor

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