The problem requires calculating the binding energy per nucleon for the given nucleus ^{20}_{10}\text{Ne}.

The binding energy per nucleon is calculated using the formula: \text{Binding energy per nucleon} = \frac{\text{Total binding energy}}{\text{Number of nucleons}}

Here, the total binding energy of ^{20}_{10}\text{Ne} is given as 160.647 \ \text{MeV}. The number of nucleons in this nucleus is 20 (as indicated by the mass number of neon).

Substituting these values into the formula:

\text{Binding energy per nucleon} = \frac{160.647}{20} = 8.032 \ \text{MeV}

Thus, the binding energy per nucleon for ^{20}_{10}\text{Ne} is 8.032 \ \text{MeV}.

This matches the option $8.032 \ MeV$.

It is key to notice how binding energy per nucleon is derived by dividing the total binding energy by the number of nucleons, a common calculation in nuclear physics problems.