Step 1: Identify the Industrial Process:
Sodium Carbonate (\( \text{Na}_2\text{CO}_3 \)), also known as washing soda, is industrially prepared by the Solvay Process (Ammonia-Soda process).
Step 2: Why other options are incorrect:
(A) Deacon's process: Used for the manufacture of Chlorine (\( \text{Cl}_2 \)).
(B) Castner-Kellner process: Used for the manufacture of Sodium Hydroxide (\( \text{NaOH} \)).
(C) Nelson cell process: Also used for the manufacture of Sodium Hydroxide (\( \text{NaOH} \)).