A `[M(H_(2)O)_(6)]^(2+)` complex typically absorbs at around 600 n. it is allowed to react with ammonia to form a new compelx `[M(NH_(3))_(6)]^(2+)` that should have absorption at:

Options

A. 800 nm
B. 580 nm
C. 620 nm
D. 320 nm

Explanation

To solve the problem, we need to analyze the absorption properties of the two complexes, `[M(H₂O)₆]²⁺` and `[M(NH₃)₆]²⁺`, in terms of their ligand field strengths and how they affect the crystal field splitting energy.

### Step-by-Step Solution:

1. **Identify the Initial Complex and Its Absorption:**
- The complex `[M(H₂O)₆]²⁺` absorbs light at around 600 nm. This indicates the energy difference between the split d-orbitals (Δ) corresponds to this wavelength.

2. **Understand Ligand Strength:**
- Water (H₂O) is a weaker field ligand compared to ammonia (NH₃). The strength of a ligand affects the crystal field splitting energy (Δ). Stronger ligands cause greater splitting of the d-orbitals.

3. **Reaction with Ammonia:**
- When the complex reacts with ammonia, it forms a new complex `[M(NH₃)₆]²⁺`. Since ammonia is a stronger ligand than water, the crystal field splitting energy (Δ) will increase.

4. **Effect on Absorption Wavelength:**
- As the crystal field splitting energy increases, the wavelength of light absorbed will decrease. This is because the energy of the absorbed light (E = hc/λ) is directly related to the splitting energy (Δ). Therefore, a higher Δ corresponds to a lower λ.

5. **Calculate the New Absorption Wavelength:**
- Since the original complex absorbs at 600 nm and the new complex has a stronger ligand (NH₃), the absorption will shift to a shorter wavelength. The next nearest lower wavelength is 580 nm.

6. **Conclusion:**
- The new complex `[M(NH₃)₆]²⁺` will absorb at approximately **580 nm**.

### Final Answer:
The absorption for the complex `[M(NH₃)₆]²⁺` will be at **580 nm**.

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