Step 1: Understanding the Question:
The problem asks for the color change observed during a precipitation titration of $\mathrm{NaCl}$ with $\mathrm{AgNO}_3$ utilizing fluorescein as an adsorption indicator (Fajans method).
Step 2: Key Formula or Approach:
Fajans method relies on the behavior of adsorption indicators. Before the equivalence point, the precipitate particles are negatively charged due to the adsorption of excess lattice ions. After the equivalence point, excess titrant ions impart a positive charge, causing the indicator dye to adsorb and change color.
Step 3: Detailed Explanation:
Initially, when $\mathrm{AgNO}_3$ is added to $\mathrm{NaCl}$, a precipitate of $\mathrm{AgCl}$ forms. Fluorescein in the solution imparts a pale greenish-yellow or pale yellow color.
Before the equivalence point, $\mathrm{Cl}^-$ ions are in excess and adsorb onto the surface of $\mathrm{AgCl}$, forming a primary layer of negative charge: $(\mathrm{AgCl})\cdot\mathrm{Cl}^-$. The negatively charged fluorescein dye anions are repelled by this surface.
Exactly at the equivalence point and just after it, $\mathrm{Ag}^+$ ions become in excess and adsorb onto the precipitate surface, turning it positive: $(\mathrm{AgCl})\cdot\mathrm{Ag}^+$.
The negatively charged fluorescein dye anions are now strongly attracted to this positively charged layer. Upon adsorption, a modified electronic structure or surface complex forms, changing the visible color from pale yellow to a distinct reddish-pink on the precipitate surface.
Step 4: Final Answer:
The color change observed is from pale yellow to reddish pink, matching option (B).