Coordination compounds plays many important roles in animals and plants. The are essential in the storage and transport of oxygen as electrons transfer agents as catalysts and in photosynthesis Wide range of application in daily life takes place through formation of complexes Photographic fixing qualitative and quantitative analysis purification of water metallurgical extraction are some specific worth mentioning
The complex `[Fe(H_(2)O)_(5)NO]^(2+)` is formed in the brown ring test for nitrates when freshly prepared `FeSO_(4)` soultion is added to aqueous solution of `NO_(3)^(Θ)` followed by addition of conc. `H_(2)SO_(4)` Select correct statement about this complex
(a) Colour change is due to charge transfer
(b) It has iron in `+1` oxidation state and nitrosyl as `NO^(o+)`
(c ) It has magnetic moment of `3.87BM` confirming three unpaired electrons in Fe
(a) All the above are correct statements .

Answer

To solve the question regarding the complex \([Fe(H_2O)_5NO]^{2+}\) formed in the brown ring test for nitrates, we need to analyze each of the statements provided in the question.

### Step 1: Analyze the Color Change
The first statement claims that the color change is due to charge transfer.
- Charge transfer can occur in coordination compounds either from the ligand to the metal (ligand-to-metal charge transfer) or from the metal to the ligand (metal-to-ligand charge transfer).
- In the case of the complex \([Fe(H_2O)_5NO]^{2+}\), the color change observed is indeed due to charge transfer, specifically from the nitrosyl ligand (NO) to the iron center.
- Therefore, **this statement is correct**.

### Step 2: Determine the Oxidation State of Iron
The second statement claims that iron is in the +1 oxidation state and nitrosyl (NO) is in the +1 oxidation state.
- To find the oxidation state of iron (let's denote it as \(X\)), we can set up the equation based on the charges:
\[ X + 5(0) + (+1) = +2 \]
where the oxidation state of \(H_2O\) is 0 and that of \(NO\) is +1.
- Solving for \(X\):
\[ X + 1 = 2 \implies X = +1 \]
- Therefore, iron is indeed in the +1 oxidation state, and nitrosyl (NO) is also in the +1 oxidation state.
- **This statement is also correct**.

### Step 3: Calculate the Magnetic Moment
The third statement claims that the magnetic moment is 3.87 BM, confirming three unpaired electrons in iron.
- The electronic configuration of iron (Fe) is \( [Ar] 3d^6 4s^2 \). For \(Fe^{+1}\), the configuration becomes \(3d^6 4s^1\) (removing one electron from the 4s orbital).
- In the \(3d\) subshell, there are 6 electrons. The distribution of these electrons in the \(3d\) orbitals will lead to three unpaired electrons (due to Hund's rule).
- The formula for calculating the magnetic moment (\(\mu\)) is:
\[ \mu = \sqrt{n(n + 2)} \]
where \(n\) is the number of unpaired electrons. Here, \(n = 3\):
\[ \mu = \sqrt{3(3 + 2)} = \sqrt{15} \approx 3.87 \, \text{BM} \]
- Thus, the magnetic moment of 3.87 BM confirms that there are three unpaired electrons.
- **This statement is also correct**.

### Conclusion
Since all three statements (a, b, and c) are correct, the correct answer is:
**(d) All the above are correct statements.**