Amongst `[TiE_(6)]^(2-), [CoF_(6)]^(3-), Cu_(2)Cl_(2)` and `[NiCl_(4)]^(2-)` [Atomic no. `Ti = 22, Co = 27, Cu = 29, Ni = 28`] the colourless species are :
(A) `[TiF_(6)]^(2-)` and `[Cu_(2)Cl_(2)]`
(B) `Cu_(2)Cl_(2)` and `[NiCl_(4)]^(2-)`
(C) `[TiF_(6)]^(2-)` and `[CoF_(6)]^(3-)`
(D) `[CoF_(6)]^(3-)` and `[NiCl_(4)]^(2-)`

Options

A. `CoF_(6)^(3-) and NiCl_(4)^(2-)`
B. `TiF_(6)^(2-) and CoF_(6)^(3-)`
C. `NiCl_(4)^(2-) and Cu_(2)Cl_(2)`
D. `TiF_(6)^(2-) and Cu_(2)Cl_(2)`

Answer

To determine which of the given species are colorless, we need to analyze the oxidation states of the metals in each complex and their electron configurations. Colorless species typically have no unpaired electrons, which means they do not undergo d-d transitions that lead to color.

### Step-by-Step Solution:

1. **Identify the oxidation state and electron configuration of each complex:**
- **For `[TiF_(6)]^(2-)`:**
- Let the oxidation state of Ti be \( x \).
- The equation is \( x + 6(-1) = -2 \) (since F has a -1 charge).
- Thus, \( x - 6 = -2 \) → \( x = +4 \).
- The electron configuration of Ti in the +4 state is \( [Ar] 3d^0 \) (no unpaired electrons).

- **For `[CoF_(6)]^(3-)`:**
- Let the oxidation state of Co be \( x \).
- The equation is \( x + 6(-1) = -3 \).
- Thus, \( x - 6 = -3 \) → \( x = +3 \).
- The electron configuration of Co in the +3 state is \( [Ar] 3d^6 \) (has unpaired electrons).

- **For `Cu_(2)Cl_(2)`:**
- Let the oxidation state of Cu be \( x \).
- The equation is \( 2x + 2(-1) = 0 \).
- Thus, \( 2x - 2 = 0 \) → \( 2x = 2 \) → \( x = +1 \).
- The electron configuration of Cu in the +1 state is \( [Ar] 3d^{10} \) (no unpaired electrons).

- **For `[NiCl_(4)]^(2-)`:**
- Let the oxidation state of Ni be \( x \).
- The equation is \( x + 4(-1) = -2 \).
- Thus, \( x - 4 = -2 \) → \( x = +2 \).
- The electron configuration of Ni in the +2 state is \( [Ar] 3d^8 \) (has unpaired electrons).

2. **Determine which species are colorless:**
- `[TiF_(6)]^(2-)`: Colorless (3d^0, no unpaired electrons).
- `[CoF_(6)]^(3-)`: Colored (3d^6, has unpaired electrons).
- `Cu_(2)Cl_(2)`: Colorless (3d^{10}, no unpaired electrons).
- `[NiCl_(4)]^(2-)`: Colored (3d^8, has unpaired electrons).

3. **Conclusion:**
- The colorless species are `[TiF_(6)]^(2-)` and `Cu_(2)Cl_(2)`.

### Final Answer:
The colorless species are option (A) `[TiF_(6)]^(2-)` and `Cu_(2)Cl_(2)`.