Step 1: Identification
The configuration $1s^{2}, 2s^{2}, 2p^{6}, 3s^{1}$ belongs to Sodium ($Na$, $Z=11$).
Step 2: Classification
Sodium is an alkali metal (Group 1).
Step 3: Property
Oxides of highly electropositive metals, especially alkali metals, are strongly basic in nature.
Step 4: Conclusion
Thus, the oxide ($Na_{2}O$) is basic.
Final Answer: (c)