To determine which group elements of the first transition series have the highest paramagnetism in elemental form for +1, +2, and +3 oxidation states, we need to analyze the electronic configurations of the elements in the first transition series and their respective oxidation states.
### Step-by-Step Solution:
1. **Identify the First Transition Series:**
The first transition series includes the following elements:
- Scandium (Sc, Z=21)
- Titanium (Ti, Z=22)
- Vanadium (V, Z=23)
- Chromium (Cr, Z=24)
- Manganese (Mn, Z=25)
- Iron (Fe, Z=26)
- Cobalt (Co, Z=27)
- Nickel (Ni, Z=28)
- Copper (Cu, Z=29)
- Zinc (Zn, Z=30)
2. **Determine the Oxidation States:**
We will analyze the +1, +2, and +3 oxidation states for the elements in the first transition series.
3. **+1 Oxidation State:**
- **Scandium (Sc)**: In +1 state, the configuration is \( [Ar] 4s^2 3d^0 \) → 0 unpaired electrons (0 paramagnetism).
- **Titanium (Ti)**: In +1 state, the configuration is \( [Ar] 4s^2 3d^1 \) → 1 unpaired electron (1 paramagnetic).
- **Vanadium (V)**: In +1 state, the configuration is \( [Ar] 4s^2 3d^2 \) → 2 unpaired electrons (2 paramagnetic).
- **Chromium (Cr)**: In +1 state, the configuration is \( [Ar] 4s^1 3d^5 \) → 6 unpaired electrons (6 paramagnetic).
- **Manganese (Mn)**: In +1 state, the configuration is \( [Ar] 4s^2 3d^5 \) → 5 unpaired electrons (5 paramagnetic).
- **Iron (Fe)**: In +1 state, the configuration is \( [Ar] 4s^2 3d^6 \) → 4 unpaired electrons (4 paramagnetic).
- **Cobalt (Co)**: In +1 state, the configuration is \( [Ar] 4s^2 3d^7 \) → 3 unpaired electrons (3 paramagnetic).
- **Nickel (Ni)**: In +1 state, the configuration is \( [Ar] 4s^2 3d^8 \) → 2 unpaired electrons (2 paramagnetic).
- **Copper (Cu)**: In +1 state, the configuration is \( [Ar] 4s^1 3d^{10} \) → 1 unpaired electron (1 paramagnetic).
- **Zinc (Zn)**: In +1 state, the configuration is \( [Ar] 4s^2 3d^{10} \) → 0 unpaired electrons (0 paramagnetism).
**Conclusion for +1 O.S:** Chromium (Cr) has the highest paramagnetism with 6 unpaired electrons.
4. **+2 Oxidation State:**
- **Scandium (Sc)**: In +2 state, the configuration is \( [Ar] 4s^2 3d^0 \) → 0 unpaired electrons.
- **Titanium (Ti)**: In +2 state, the configuration is \( [Ar] 4s^0 3d^2 \) → 2 unpaired electrons.
- **Vanadium (V)**: In +2 state, the configuration is \( [Ar] 4s^0 3d^3 \) → 3 unpaired electrons.
- **Chromium (Cr)**: In +2 state, the configuration is \( [Ar] 4s^0 3d^4 \) → 4 unpaired electrons.
- **Manganese (Mn)**: In +2 state, the configuration is \( [Ar] 4s^0 3d^5 \) → 5 unpaired electrons.
- **Iron (Fe)**: In +2 state, the configuration is \( [Ar] 4s^0 3d^6 \) → 4 unpaired electrons.
- **Cobalt (Co)**: In +2 state, the configuration is \( [Ar] 4s^0 3d^7 \) → 3 unpaired electrons.
- **Nickel (Ni)**: In +2 state, the configuration is \( [Ar] 4s^0 3d^8 \) → 2 unpaired electrons.
- **Copper (Cu)**: In +2 state, the configuration is \( [Ar] 4s^0 3d^9 \) → 1 unpaired electron.
- **Zinc (Zn)**: In +2 state, the configuration is \( [Ar] 4s^0 3d^{10} \) → 0 unpaired electrons.
**Conclusion for +2 O.S:** Manganese (Mn) has the highest paramagnetism with 5 unpaired electrons.
5. **+3 Oxidation State:**
- **Scandium (Sc)**: In +3 state, the configuration is \( [Ar] 4s^0 3d^0 \) → 0 unpaired electrons.
- **Titanium (Ti)**: In +3 state, the configuration is \( [Ar] 4s^0 3d^1 \) → 1 unpaired electron.
- **Vanadium (V)**: In +3 state, the configuration is \( [Ar] 4s^0 3d^2 \) → 2 unpaired electrons.
- **Chromium (Cr)**: In +3 state, the configuration is \( [Ar] 4s^0 3d^3 \) → 3 unpaired electrons.
- **Manganese (Mn)**: In +3 state, the configuration is \( [Ar] 4s^0 3d^4 \) → 4 unpaired electrons.
- **Iron (Fe)**: In +3 state, the configuration is \( [Ar] 4s^0 3d^5 \) → 5 unpaired electrons.
- **Cobalt (Co)**: In +3 state, the configuration is \( [Ar] 4s^0 3d^6 \) → 4 unpaired electrons.
- **Nickel (Ni)**: In +3 state, the configuration is \( [Ar] 4s^0 3d^7 \) → 3 unpaired electrons.
- **Copper (Cu)**: In +3 state, the configuration is \( [Ar] 4s^0 3d^8 \) → 2 unpaired electrons.
- **Zinc (Zn)**: In +3 state, the configuration is \( [Ar] 4s^0 3d^9 \) → 1 unpaired electron.
**Conclusion for +3 O.S:** Iron (Fe) has the highest paramagnetism with 5 unpaired electrons.
### Final Summary:
- For +1 O.S: Chromium (Cr)
- For +2 O.S: Manganese (Mn)
- For +3 O.S: Iron (Fe)
