Un-decomposed silver bromide from developed film, in black and white photography, makes a complex with hypo. The formula of the complex is

$[Ag(S_2O_3)_2]^{3-}$

The correct answer is Option (1) → $[Ag(S_2O_3)_2]^{3-}$

1. Identify the Fixing Agent

In photography, the "fixing" process removes unexposed and un-decomposed silver bromide from the film so the image doesn't darken over time. The chemical used for this is sodium thiosulfate ($Na_2S_2O_3$), commonly known as hypo.

2. Understand the Chemical Reaction

When the film is washed with the hypo solution, the silver ions ($Ag^+$) from the insoluble silver bromide react with the thiosulfate ions ($S_2O_3^{-2}$) to form a water-soluble coordination complex.

The balanced chemical equation for this reaction is:

$AgBr(s)+2Na_2S_2O_3(aq)→Na_3[Ag(S_2O_3)_2](aq)+NaBr(aq)$

3. Determine the Complex Ion Formula

The resulting complex, sodium bis(thiosulfato)argentate(I), dissociates in solution to release the following complex ion:

• Formula: $[Ag(S_2O_3)_2]^{-3}$
• Charge Calculation: Silver (Ag) has an oxidation state of +1. Each thiosulfate ($S_2O_3$) ligand has a charge of -2. Therefore, the total charge is: (+1) + 2(-2) = -3

4. Conclusion

The formation of this soluble complex allows the un-decomposed silver salts to be washed away, leaving only the metallic silver image on the negative.