`[Ti(H_(2)O)_(6)]^(3+)` absorbs light of wavelength 500Å. Name one ligand whih would form a titanium (III) complex absorbing light to lower wavelength than 500Å and one ligand which would form a complex absorbing light of wavelength higher than 500 Å.

Answer

To solve the problem, we need to identify ligands that will influence the absorption of light by the titanium (III) complex, specifically in relation to the given wavelength of 500 Å.

### Step-by-Step Solution:

1. **Understanding the Absorption of Light**:
- The complex `[Ti(H₂O)₆]³⁺` absorbs light at a wavelength of 500 Å.
- The energy of the absorbed light can be calculated using the formula:
\[ E = \frac{hc}{\lambda} \]
where \( E \) is energy, \( h \) is Planck's constant, \( c \) is the speed of light, and \( \lambda \) is the wavelength.

2. **Determining Energy and Wavelength Relationship**:
- Since energy is inversely proportional to wavelength, a lower wavelength corresponds to higher energy and vice versa.
- Therefore, ligands that cause a greater splitting of the d-orbitals will absorb light at shorter wavelengths (higher energy).

3. **Identifying Ligands**:
- We need to find one ligand that will cause the titanium (III) complex to absorb light at a wavelength lower than 500 Å and one that will cause it to absorb at a wavelength higher than 500 Å.
- Ligands can be classified based on their field strength:
- **Weak Field Ligands**: These cause less splitting of d-orbitals and absorb longer wavelengths (lower energy).
- **Strong Field Ligands**: These cause greater splitting and absorb shorter wavelengths (higher energy).

4. **Choosing Ligands**:
- For a ligand that absorbs light at a wavelength lower than 500 Å (strong field ligand), we can choose **CN⁻ (cyanide)**.
- For a ligand that absorbs light at a wavelength higher than 500 Å (weak field ligand), we can choose **F⁻ (fluoride)**.

5. **Final Answer**:
- Ligand for absorbing light at a wavelength lower than 500 Å: **CN⁻ (cyanide)**
- Ligand for absorbing light at a wavelength higher than 500 Å: **F⁻ (fluoride)**