Question

The potential energy shared by two atoms separated by a distance r in a diatomic molecule is given by the Lennard-Jones function (?0 and ?0 are constants): ?(?) = ?0 [( ?0/?)^12 − 2( ?0/? )^6 ] (a) Where is ?(?) = 0? (b) Show that the minimum potential energy is −?0 and that it occurs at ?0. (c) Where is ?? = 0 ? (d) Sketch ?(?).

Answer 1

Given the form of the potential, we have
  
a)
Let
  
  
  
  
   
   
b)
  The radial component of the force is given by
  
And the minimum of U(r) is where, .
  
  
  
     
     
And the minimum of U(r) is given by
     
   
  

c)
  The radial component of the force, i.e. is zero at the position at which the U(r) is minimum, and we have already component this above and this is given by
     
d)
  The sketch of U(r) is given by