You all fail.
A common way of approximating the potential energy curve V(R) of a bound state of a diatomic molecule is with a Morse function:
a) What happens to the function as R--> 0
b) Verify that De = V(infinity) - U(Re)
c) Verify that V'(Re) = 0
d) What is beta in terms of De and k, where k = d2V/dR2 (second derivative of V with respect to R)