The potential energy of two atoms in a molecule can be approximated by the Morse function:
U(r)=A[((e^((R-r)/s)-1)^2 )-1)] where r is the distance between the two atoms and A, R and S are positive constants with S<
a) Sketch this function for 0
b) Find the equilibrium separation r0 at which U(r) is a minimum.
c) Now write r=r0+x so that x is the displacement from equilibrium and show that for small displacements U has the approximate form: U=constant +1?2 kx2. What is k?