For the complex `K_(2)[Cr(NO)(NH_(3))(CN)_(4)],mu=1.73 BM`.
(i) Write IUPAC name.
(ii) What will be structure ?
(iii) How many unpaired electrons are present in the central metal ion ?
(iv) Is it paramagnetic or diamagnetic ?
(v) Calculate the EAN of the complex.
(vi) What will be the hybridisation of the complex.

Answer

To solve the question step by step, we will address each part of the question regarding the complex \( K_2[Cr(NO)(NH_3)(CN)_4] \).

### Step 1: Write the IUPAC Name
The complex consists of potassium ions and a coordination complex. The ligands are nitroso (NO), ammonia (NH3), and cyanide (CN). The IUPAC name is constructed by naming the ligands in alphabetical order followed by the name of the metal with its oxidation state.

**IUPAC Name:** Potassium tetra-cyanonitroso-aminochromate(1).

### Step 2: Determine the Structure
The complex has six ligands: one nitroso, one ammonia, and four cyanide ligands. Since it has six coordination sites, it adopts an octahedral geometry.

**Structure:** Octahedral.

### Step 3: Count Unpaired Electrons
The magnetic moment (\( \mu \)) is given as 1.73 BM. The formula for magnetic moment is:
\[ \mu = \sqrt{n(n + 2)} \]
Where \( n \) is the number of unpaired electrons.

Setting \( \mu = 1.73 \):
\[ 1.73 = \sqrt{n(n + 2)} \]
Squaring both sides:
\[ 1.73^2 = n(n + 2) \implies 2.9929 = n^2 + 2n \]
Rearranging gives:
\[ n^2 + 2n - 2.9929 = 0 \]
Using the quadratic formula:
\[ n = \frac{-2 \pm \sqrt{(2)^2 - 4 \cdot 1 \cdot (-2.9929)}}{2 \cdot 1} \]
Calculating gives \( n \approx 1 \).

**Unpaired Electrons:** 1.

### Step 4: Paramagnetic or Diamagnetic
Since there is one unpaired electron, the complex is paramagnetic.

**Paramagnetic or Diamagnetic:** Paramagnetic.

### Step 5: Calculate the Effective Atomic Number (EAN)
The EAN is calculated using the formula:
\[ \text{EAN} = Z + 2n - c \]
Where:
- \( Z \) = Atomic number of the metal (Chromium, \( Z = 24 \))
- \( n \) = Number of ligands (6 ligands, each donating 2 electrons)
- \( c \) = Charge on the complex (the oxidation state of Cr is +1, thus -1 for the complex)

Calculating:
\[ \text{EAN} = 24 + 2(6) - 1 = 24 + 12 - 1 = 35 \]

**EAN:** 35.

### Step 6: Determine Hybridization
For an octahedral complex with six ligands, the hybridization can be determined. The presence of strong field ligands (like CN and NH3) suggests that the hybridization involves d-orbitals.

**Hybridization:** \( d^2sp^3 \).

### Summary of Answers
1. **IUPAC Name:** Potassium tetra-cyanonitroso-aminochromate(1).
2. **Structure:** Octahedral.
3. **Unpaired Electrons:** 1.
4. **Paramagnetic or Diamagnetic:** Paramagnetic.
5. **EAN:** 35.
6. **Hybridization:** \( d^2sp^3 \).