Match the ions of Column-I with the properties of Column-II
Column-I Column-II
(A) `Mn^(2+)` (p) Diamagnetic
( B) `V^(3+)` ( q ) Paramagnetic
( C ) `Zn^(2+)` ( r ) Colourless compounds
( D ) `Ti^(4+)` ( s ) Magnetic moment = 2.82 BM

Answer

To solve the problem of matching the ions from Column-I with the properties in Column-II, we will analyze the electronic configurations of the given ions and determine their magnetic properties and color characteristics.

### Step-by-Step Solution:

1. **Identify the Electronic Configurations:**
- **(A) `Mn^(2+)`:**
- Atomic number of Mn = 25
- Ground state configuration: `Ar 4s^2 3d^5`
- For `Mn^(2+)`, two electrons are removed from the 4s subshell:
- Configuration: `Ar 4s^0 3d^5`
- Unpaired electrons = 5 (paramagnetic)

- **(B) `V^(3+)`:**
- Atomic number of V = 23
- Ground state configuration: `Ar 4s^2 3d^3`
- For `V^(3+)`, three electrons are removed (2 from 4s and 1 from 3d):
- Configuration: `Ar 4s^0 3d^2`
- Unpaired electrons = 2 (paramagnetic)

- **(C) `Zn^(2+)`:**
- Atomic number of Zn = 30
- Ground state configuration: `Ar 4s^2 3d^{10}`
- For `Zn^(2+)`, two electrons are removed from 4s:
- Configuration: `Ar 4s^0 3d^{10}`
- Unpaired electrons = 0 (diamagnetic)

- **(D) `Ti^(4+)`:**
- Atomic number of Ti = 22
- Ground state configuration: `Ar 4s^2 3d^2`
- For `Ti^(4+)`, four electrons are removed (2 from 4s and 2 from 3d):
- Configuration: `Ar 4s^0 3d^0`
- Unpaired electrons = 0 (diamagnetic)

2. **Match with Properties:**
- **(A) `Mn^(2+)`:**
- Unpaired electrons = 5 (paramagnetic)
- Matches with (q) Paramagnetic.

- **(B) `V^(3+)`:**
- Magnetic moment = 2.82 BM (calculated as `√(2(2+2))`)
- Matches with (s) Magnetic moment = 2.82 BM.

- **(C) `Zn^(2+)`:**
- Unpaired electrons = 0 (diamagnetic) and forms colorless compounds.
- Matches with (r) Colorless compounds.

- **(D) `Ti^(4+)`:**
- Unpaired electrons = 0 (diamagnetic) and forms colorless compounds.
- Matches with (p) Diamagnetic.

### Final Matches:
- **(A) `Mn^(2+)` → (q) Paramagnetic**
- **(B) `V^(3+)` → (s) Magnetic moment = 2.82 BM**
- **(C) `Zn^(2+)` → (r) Colorless compounds**
- **(D) `Ti^(4+)` → (p) Diamagnetic**