Match the property given in Column I with the element given in Column II.
`{:(,"Column I(Property)",,"Column II( Element)"),((i),"Lanthanoid which shows "+4"oxidation state",(a),P m),((ii),"lLnathanoid which can show "+2"oxidation state",(b),Ce),((iii),"Radiactive lanthaoid",(c ),Lu),((iv),"Lanthanoid which has "4f^(7)"electronic configuration in "+3"oxidation state",(d),Eu),((v),"Lanthanoid which has " 4f^(14) "electronic configuration in "+3"oxidation state",(e ) ,Gd),(,,(f ),Dy):}`

Answer

To match the properties given in Column I with the elements in Column II, we will analyze each property and determine the corresponding lanthanoid element based on their oxidation states and electronic configurations.

### Step-by-Step Solution:

1. **Property (i): Lanthanoid which shows +4 oxidation state.**
- The element that shows a +4 oxidation state is **Cerium (Ce)**. Cerium can lose four electrons from its outer shell to achieve this oxidation state.
- **Match:** (i) → (b) Ce

2. **Property (ii): Lanthanoid which can show +2 oxidation state.**
- The lanthanoid that can show a +2 oxidation state is **Europium (Eu)**. Europium can lose two electrons to achieve this state.
- **Match:** (ii) → (d) Eu

3. **Property (iii): Radioactive lanthanoid.**
- The only radioactive lanthanoid among the options is **Promethium (Pm)**. Promethium is known for its radioactivity.
- **Match:** (iii) → (a) Pm

4. **Property (iv): Lanthanoid which has 4f^7 electronic configuration in +3 oxidation state.**
- The lanthanoid with a 4f^7 configuration in the +3 oxidation state is **Gadolinium (Gd)**. In the +3 state, it retains the 4f^7 configuration.
- **Match:** (iv) → (e) Gd

5. **Property (v): Lanthanoid which has 4f^14 electronic configuration in +3 oxidation state.**
- The lanthanoid that has a 4f^14 configuration in the +3 oxidation state is **Lutetium (Lu)**. In this state, it retains the fully filled 4f^14 configuration.
- **Match:** (v) → (c) Lu

### Final Matches:
- (i) → (b) Ce
- (ii) → (d) Eu
- (iii) → (a) Pm
- (iv) → (e) Gd
- (v) → (c) Lu