Step 1: Understanding Plaster of Paris.
Plaster of Paris (\text{CaSO}_4 \cdot \frac{1}{2} H_2O) is used in orthopedics for setting broken bones. When mixed with water, it hardens into solid gypsum.
\[
\text{CaSO}_4 \cdot \frac{1}{2} H_2O + H_2O \rightarrow \text{CaSO}_4 \cdot 2H_2O
\]
Step 2: Explanation of incorrect options.
- Washing soda (\text{Na}_2\text{CO}_3) is used in cleaning.
- Quicklime (\text{CaO}) is used in cement but not in bone setting.
- Gypsum (\text{CaSO}_4 \cdot 2H_2O) is a natural form of calcium sulfate but does not set like Plaster of Paris.