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Evaluating the location r_m of the minimum of potential

  1. Nov 3, 2015 #1
    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. jcsd
  3. Nov 3, 2015 #2

    DrClaude

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    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.
     
  4. Nov 3, 2015 #3
    my question was how do i evaluate the location of r_m of the minimum potential.
     
  5. Nov 3, 2015 #4

    mfb

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    Staff: Mentor

    Like this:
     
  6. Nov 3, 2015 #5
    so basically the location of r_m would be -4(epsilon)[(-12(delta^12)/r^13 + 6delta^6/r^7]
     
  7. Nov 3, 2015 #6

    mfb

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    Staff: Mentor

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