Step 1: Understand the Problem.
The atomic mass of oxygen ($ \text{O} $) is approximately $ 16.00 \, \text{g/mol} $. To find the mass of $ 0.5 $ moles of oxygen atoms, use the formula:
\[
\text{Mass} = \text{Number of moles} \times \text{Molar mass}.
\]
Step 2: Calculate the Mass.
Substitute the given values:
\[
\text{Mass} = 0.5 \, \text{mol} \times 16.00 \, \text{g/mol} = 8.00 \, \text{g}.
\]
Step 3: Analyze the Options.
Option (1): $ 10 \, \text{g} $ — Incorrect, as the calculated mass is $ 8.00 \, \text{g} $.
Option (2): $ 12 \, \text{g} $ — Incorrect, as the calculated mass is $ 8.00 \, \text{g} $.
Option (3): $ 14 \, \text{g} $ — Incorrect, as the calculated mass is $ 8.00 \, \text{g} $.
Option (4): $ 8 \, \text{g} $ — Correct, as it matches the calculated value.
Step 4: Final Answer.
\[
\boxed{(4) \quad 8 \, \text{g}}
\]