Consider the following complex `[Co(NH_(3))_(5)CO_(3)]ClO_(4)`
The coordination number, oxidation number number of d-electrons and number of unpaired d-electrons on the metal are respectively

Options

A. `{:("Coordination no.","Oxidation no.","No. of d-electrons","Unpaired d-electron"),(6,3,6,0):}`
B. `{:("Coordination no.","Oxidation no.","No. of d-electrons","Unpaired d-electron"),(7,2,7,1):}`
C. `{:("Coordination no.","Oxidation no.","No. of d-electrons","Unpaired d-electron"),(7,1,6,4):}`
D. `{:("Coordination no.","Oxidation no.","No. of d-electrons","Unpaired d-electron"),(6,2,7,3):}`

Answer

To solve the problem step by step, we will analyze the coordination complex \([Co(NH_3)_5CO_3]ClO_4\).

### Step 1: Determine the Coordination Number
The coordination number is defined as the total number of ligand atoms that are bonded to the central metal atom.

In this complex:
- There are 5 ammonia (NH₃) ligands, each contributing one coordination site.
- There is 1 carbonate (CO₃) ligand, which also contributes one coordination site.

Thus, the coordination number is:
\[ \text{Coordination Number} = 5 + 1 = 6 \]

### Step 2: Calculate the Oxidation Number of Cobalt
To find the oxidation number of cobalt (Co) in the complex, we can set up an equation based on the overall charge of the complex. The complex is neutral, and the anion \([ClO_4]^-\) has a charge of -1.

Let the oxidation state of cobalt be \(x\):
\[ x + (5 \times 0) + (-2) + (-1) = 0 \]
Where:
- The oxidation state of NH₃ is 0 (neutral ligand).
- The oxidation state of CO₃ is -2.

This simplifies to:
\[ x - 2 - 1 = 0 \implies x - 3 = 0 \implies x = +3 \]

Thus, the oxidation number of cobalt is:
\[ \text{Oxidation Number} = +3 \]

### Step 3: Determine the Number of d-Electrons
Cobalt has an atomic number of 27, and its electronic configuration is:
\[ \text{Co: } [Ar] 3d^7 4s^2 \]
In the +3 oxidation state, cobalt loses 3 electrons (2 from 4s and 1 from 3d):
\[ \text{Co}^{3+}: [Ar] 3d^6 \]
Thus, the number of d-electrons in Co³⁺ is:
\[ \text{Number of d-electrons} = 6 \]

### Step 4: Determine the Number of Unpaired d-Electrons
Since NH₃ is a strong field ligand, it will cause pairing of electrons in the d-orbitals. The d-orbitals split into two sets: \(t_{2g}\) (lower energy) and \(e_g\) (higher energy).

For Co³⁺ with 6 d-electrons:
- The \(t_{2g}\) orbitals will be filled first, which can hold 6 electrons.
- The filling will be: \(t_{2g}^6\) and \(e_g^0\).

Since all 6 electrons are paired in the \(t_{2g}\) orbitals, there are no unpaired electrons:
\[ \text{Number of unpaired d-electrons} = 0 \]

### Final Summary
- Coordination Number: 6
- Oxidation Number: +3
- Number of d-electrons: 6
- Number of unpaired d-electrons: 0