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.
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