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. There are three unpaired electrons in `[Co(H_2O)_6]^(2+)` and calculated value of magnetic moment on the basis of `sqrt(n(n+2))` formula is 3.87 BM. which is lower than the expermental value of 4.40 BM. The reason for this difference is due to

Options

A. increase in number of unpaired electrons during determination
B. Some contribution of the orbital motion of the electrons to the magnetic moment
C. d-d transition
D. Experimental error

Answer

To solve the question regarding the difference between the calculated magnetic moment and the experimental value for the complex \([Co(H_2O)_6]^{2+}\), we will follow these steps:

### Step 1: Understand the Magnetic Moment Formula
The magnetic moment (\(\mu\)) due to unpaired electrons is calculated using the formula:
\[ \mu = \sqrt{n(n+2)} \text{ Bohr magneton} \]
where \(n\) is the number of unpaired electrons.

**Hint:** Remember that this formula only accounts for the spin contribution to the magnetic moment.

### Step 2: Identify the Number of Unpaired Electrons
In the complex \([Co(H_2O)_6]^{2+}\), cobalt is in the +2 oxidation state. The electronic configuration for \(Co^{2+}\) is:
\[ [Ar] 3d^7 \]
In the \(3d^7\) configuration, when filling the orbitals, we have:
- 3 electrons in three separate \(3d\) orbitals (unpaired)
- 4 electrons paired in the remaining orbitals.

Thus, there are 3 unpaired electrons.

**Hint:** Visualize the filling of the \(d\) orbitals to count the unpaired electrons correctly.

### Step 3: Calculate the Theoretical Magnetic Moment
Using \(n = 3\) (the number of unpaired electrons):
\[ \mu = \sqrt{3(3+2)} = \sqrt{3 \times 5} = \sqrt{15} \approx 3.87 \text{ Bohr magneton} \]

**Hint:** Ensure you perform the square root calculation accurately.

### Step 4: Compare with Experimental Value
The experimental magnetic moment is given as 4.40 Bohr magneton, which is higher than the calculated value of 3.87 Bohr magneton.

**Hint:** Look for reasons why the experimental value might differ from the theoretical value.

### Step 5: Identify the Reason for the Difference
The difference between the calculated and experimental values arises because the theoretical calculation only considers the spin contribution to the magnetic moment. In reality, there is also an orbital contribution due to the motion of electrons in their orbits, which is not accounted for in the spin-only formula.

Thus, the reason for the difference is:
- The contribution of the orbital motion of the electrons to the magnetic moment.

**Hint:** Remember that both spin and orbital contributions affect the total magnetic moment in real scenarios.

### Final Answer
The reason for the difference between the calculated value (3.87 BM) and the experimental value (4.40 BM) is due to the contribution of the orbital motion of the electrons to the magnetic moment.