Transition metals and many of their compounds show paramagnetic behaviour where there are unpaired electron or electrons. The magnetic moment arises from the spin and orbital motions in ions or molecule. Magnetic moment of n unpaired electrons is given as
`mu=sqrt(n(n+2))` Bohr magneton
Magnetic moment increases as the number of unpaired electrons increases.
Q. In 3d series the maximum magnetic moment is shown by

Options

A. Sc
B. V
C. Cr
D. Fe

Explanation

To determine which element in the 3d series shows the maximum magnetic moment, we will calculate the magnetic moment for each transition metal in the series based on the number of unpaired electrons using the formula:

\[ \mu = \sqrt{n(n+2)} \text{ Bohr magneton} \]

where \( n \) is the number of unpaired electrons.

### Step 1: Identify the 3d series transition metals
The 3d series transition metals include Scandium (Sc), Titanium (Ti), Vanadium (V), Chromium (Cr), Manganese (Mn), Iron (Fe), Cobalt (Co), Nickel (Ni), and Copper (Cu), and Zinc (Zn).

### Step 2: Determine the electronic configurations and number of unpaired electrons

1. **Scandium (Sc)**:
- Atomic number: 21
- Electronic configuration: \([Ar] 3d^1 4s^2\)
- Unpaired electrons: 1
- Magnetic moment:
\[ \mu = \sqrt{1(1+2)} = \sqrt{3} \text{ Bohr magneton} \]

2. **Titanium (Ti)**:
- Atomic number: 22
- Electronic configuration: \([Ar] 3d^2 4s^2\)
- Unpaired electrons: 2
- Magnetic moment:
\[ \mu = \sqrt{2(2+2)} = \sqrt{8} \text{ Bohr magneton} \]

3. **Vanadium (V)**:
- Atomic number: 23
- Electronic configuration: \([Ar] 3d^3 4s^2\)
- Unpaired electrons: 3
- Magnetic moment:
\[ \mu = \sqrt{3(3+2)} = \sqrt{15} \text{ Bohr magneton} \]

4. **Chromium (Cr)**:
- Atomic number: 24
- Electronic configuration: \([Ar] 3d^5 4s^1\)
- Unpaired electrons: 6
- Magnetic moment:
\[ \mu = \sqrt{6(6+2)} = \sqrt{48} \text{ Bohr magneton} \]

5. **Manganese (Mn)**:
- Atomic number: 25
- Electronic configuration: \([Ar] 3d^5 4s^2\)
- Unpaired electrons: 5
- Magnetic moment:
\[ \mu = \sqrt{5(5+2)} = \sqrt{35} \text{ Bohr magneton} \]

6. **Iron (Fe)**:
- Atomic number: 26
- Electronic configuration: \([Ar] 3d^6 4s^2\)
- Unpaired electrons: 4
- Magnetic moment:
\[ \mu = \sqrt{4(4+2)} = \sqrt{24} \text{ Bohr magneton} \]

7. **Cobalt (Co)**:
- Atomic number: 27
- Electronic configuration: \([Ar] 3d^7 4s^2\)
- Unpaired electrons: 3
- Magnetic moment:
\[ \mu = \sqrt{3(3+2)} = \sqrt{15} \text{ Bohr magneton} \]

8. **Nickel (Ni)**:
- Atomic number: 28
- Electronic configuration: \([Ar] 3d^8 4s^2\)
- Unpaired electrons: 2
- Magnetic moment:
\[ \mu = \sqrt{2(2+2)} = \sqrt{8} \text{ Bohr magneton} \]

9. **Copper (Cu)**:
- Atomic number: 29
- Electronic configuration: \([Ar] 3d^{10} 4s^1\)
- Unpaired electrons: 1
- Magnetic moment:
\[ \mu = \sqrt{1(1+2)} = \sqrt{3} \text{ Bohr magneton} \]

10. **Zinc (Zn)**:
- Atomic number: 30
- Electronic configuration: \([Ar] 3d^{10} 4s^2\)
- Unpaired electrons: 0
- Magnetic moment:
\[ \mu = 0 \text{ Bohr magneton} \]

### Step 3: Compare the magnetic moments
- Scandium: \(\sqrt{3}\)
- Titanium: \(\sqrt{8}\)
- Vanadium: \(\sqrt{15}\)
- Chromium: \(\sqrt{48}\) (maximum)
- Manganese: \(\sqrt{35}\)
- Iron: \(\sqrt{24}\)
- Cobalt: \(\sqrt{15}\)
- Nickel: \(\sqrt{8}\)
- Copper: \(\sqrt{3}\)
- Zinc: \(0\)

### Conclusion
The maximum magnetic moment in the 3d series is shown by **Chromium (Cr)** with a magnetic moment of \(\sqrt{48}\) Bohr magneton.

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