A very dilute acidic solution of `Cd^(2+)&Ni^(2+)` gives only yelllwo ppt. of CdS on passing `H_(2)S`, this is due to:

Options

A. solubility product `(K_(sp))` of CdS is more than that of NiS.
B. Solubility product `(K_(sp))` of CdS is less than that of NiS.
C. `Cd^(2+)` belong to II B group while `Ni^(2+)` belongs to `IV`th group
D. CdS is insoluble in yellow ammonium sulphide (YAS).

Explanation

To solve the question regarding why a very dilute acidic solution of `Cd^(2+)` and `Ni^(2+)` gives only a yellow precipitate of `CdS` upon passing `H2S`, we will follow these steps:

### Step-by-Step Solution:

1. **Understanding the Reaction**: When `H2S` is passed through the solution, it dissociates to produce sulfide ions (`S^(2-)`). These sulfide ions can react with metal cations in the solution to form metal sulfides, which may precipitate out of the solution.

2. **Identifying the Metal Cations**: The metal cations present in the solution are `Cd^(2+)` and `Ni^(2+)`. Both of these cations can form sulfides with sulfide ions.

3. **Formation of Precipitates**: The solubility products (Ksp) of the sulfides formed will determine whether a precipitate forms. The relevant sulfides are `CdS` and `NiS`. The Ksp values indicate how soluble these sulfides are in water.

4. **Comparing Ksp Values**:
- The Ksp of `CdS` is lower than that of `NiS`, which means that `CdS` is less soluble than `NiS`. Therefore, at a given concentration of sulfide ions, `CdS` will precipitate before `NiS` does.

5. **Dilute Solution Consideration**: Since the solution is very dilute, the concentrations of `Cd^(2+)` and `Ni^(2+)` are similar. However, because `CdS` has a lower Ksp, it will precipitate first when sulfide ions are introduced.

6. **Conclusion**: The formation of the yellow precipitate of `CdS` indicates that the concentration of sulfide ions was sufficient to exceed the solubility product of `CdS` before it exceeded that of `NiS`. Thus, the reason only `CdS` precipitates is that the Ksp of `CdS` is less than that of `NiS`.

### Final Answer:
The yellow precipitate of `CdS` forms because the solubility product (Ksp) of `CdS` is less than that of `NiS`.