Computed potential-energy values U for a diatomic molecule C–D are listed below. Zero energy is defined at infinite separation.
r (nm) | U (kJ·mol⁻¹)
0.10 | +950
0.14 | +120
0.18 | –210
0.22 | –320
0.26 | –280
0.30 | –150
0.34 | –20
(a) On axes you provide, sketch a qualitative plot of U versus r, clearly labelling each data point.
(b) From the data, estimate the equilibrium bond length and the bond energy of C–D.
(c) Use linear interpolation between the two most negative data points to obtain a more precise value of r at which U is minimum. Show your work.
(d) The molecule vibrates so that r oscillates between 0.22 nm and 0.30 nm. Using your equilibrium value from part (b), calculate the amplitude of the vibrational displacement.