Given that the energy of the photons of different colours decreases in the order of VIBGYOR (Violet ` gt ` Indigo `gt` Blue `gt` Green ` gt ` Yellow `gt` Red ) and that if complex absorbs a photon of low energy then it shows colour of high energy photon. If an ion , `M^(2+)`, forms the complexes `[M(H_(2)O)_(6)]^(2+),[MBr_(6)]^(4-), and [M(en)_(3)]^(2+)`. The colours of the complexes, though not necessarily in order, are green, red, and blue. Match the complexes with the appropriate colour. ( Do not use the table of complementry colours for this question )

Options

A. Green, blue and red
B. Blue, and greenn
C. Green, red and blue
D. Red, blue and green

Answer

To solve the problem, we will analyze the complexes formed by the ion \( M^{2+} \) and determine their colors based on the ligand strength and the energy of the photons they absorb.

### Step-by-Step Solution:

1. **Identify the Ligands and Their Strengths**:
- The ligands involved are:
- \( H_2O \) (water)
- \( Br^- \) (bromide)
- \( en \) (ethylenediamine)
- The order of ligand strength (from strongest to weakest) is:
- \( en > H_2O > Br^- \)

2. **Understand the Relationship Between Ligand Strength and Splitting Energy**:
- In octahedral complexes, the splitting energy (\( \Delta \)) is directly proportional to the strength of the ligand. Stronger ligands cause greater splitting of the d-orbitals.
- Therefore, for our ligands:
- \( \Delta_{en} > \Delta_{H_2O} > \Delta_{Br} \)

3. **Determine the Colors Based on Absorption**:
- The color observed by a complex is the complementary color of the light it absorbs. If a complex absorbs lower energy light, it will appear as a higher energy color.
- The order of photon energy (from high to low) is: Violet > Indigo > Blue > Green > Yellow > Red.
- Thus, the corresponding colors of the complexes will be:
- **For \( en \)**: Absorbs high energy (violet/blue), appears red (low energy).
- **For \( H_2O \)**: Absorbs intermediate energy (green), appears green.
- **For \( Br^- \)**: Absorbs low energy (red), appears blue (high energy).

4. **Match the Complexes with Their Colors**:
- \( [M(H_2O)_6]^{2+} \) will show green color (intermediate energy absorption).
- \( [MBr_6]^{4-} \) will show blue color (absorbs red).
- \( [M(en)_3]^{2+} \) will show red color (absorbs violet/blue).

### Final Matching:
- \( [M(H_2O)_6]^{2+} \) → Green
- \( [MBr_6]^{4-} \) → Blue
- \( [M(en)_3]^{2+} \) → Red