= Solution
The <ground-state dissociation energy> starts at the lowest vibrational level, rather than the minimum of the potential. The <zero-point energy> of the <Morse oscillator> is
$$
E_0=hc\widetilde\omega\left(\frac12-\frac{x_e}{4}\right)=D_e(2x_e-x_e^2).
$$
Subtracting it from the <bond potential-well depth> gives
$$
\boxed{D_0=D_e-E_0=D_e(1-2x_e+x_e^2)=D_e(1-x_e)^2.}
$$
This distinction matters whenever a dissociation <energy> is inferred from a vibrational spectrum.
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