Select the correct code about complex `[Cr(NO_(2))(NH_(3))_(5)][ZnCl_(4)] :`
`(I)` IUPAC name of compoun is pentaamminenitrito`-N-`chromium `(III)` tetrachlorozincate `(II)`
`(II)` It shows geometrical isomerism
`(III)` It shows linkage isomerism
`(IV)` It shows coordination isomerism`

Options

A. III, IV
B. I, III, IV
C. II, III and IV
D. I, II, III and IV

Explanation

To solve the question regarding the complex \([Cr(NO_2)(NH_3)_5][ZnCl_4]\), we will analyze each statement provided in the question step by step.

### Step 1: Determine the IUPAC Name
The complex can be broken down into its constituent parts:
- The cationic part is \([Cr(NO_2)(NH_3)_5]^3+\)
- The anionic part is \([ZnCl_4]^{2-}\)

1. **Identify the ligands:**
- \(NH_3\) is called "ammine."
- \(NO_2\) can act as a nitro ligand or nitrito ligand depending on how it coordinates. In this case, it is coordinated through nitrogen, so it is called "nitrito-N."
- \(Cl\) is called "chloro."

2. **Count the ligands:**
- There are five \(NH_3\) ligands, so we use "penta."
- There is one \(NO_2\) ligand, so we use "nitrito-N."
- The metal in the cation is chromium, which has an oxidation state of +3.
- The anionic part has four \(Cl\) ligands, so we use "tetrachloro."

3. **Construct the name:**
- The full IUPAC name is: **pentaamminenitrito-N-chromium(III) tetrachlorozincate(II)**.

### Conclusion for Statement I
**Statement I is true.**

### Step 2: Geometrical Isomerism
To show geometrical isomerism, there must be at least two similar ligands that can occupy different positions around the central metal ion.

- In our complex, the ligands are five \(NH_3\) (which are identical) and one \(NO_2\) (which is different).
- The anionic part has four \(Cl\) ligands, which are also identical.

Since there is only one type of nitro ligand and the \(NH_3\) ligands are all the same, geometrical isomerism cannot occur.

### Conclusion for Statement II
**Statement II is false.**

### Step 3: Linkage Isomerism
Linkage isomerism occurs when a ligand can coordinate to the metal in more than one way.

- The nitrito ligand can coordinate through either the nitrogen atom (as nitrito-N) or the oxygen atom (as nitrito-O). This means that linkage isomerism is possible.

### Conclusion for Statement III
**Statement III is true.**

### Step 4: Coordination Isomerism
Coordination isomerism occurs when there is an exchange of ligands between the cationic and anionic parts of the complex.

- In this case, we can have different arrangements of ligands between the chromium and zinc parts. Thus, coordination isomerism is also possible.

### Conclusion for Statement IV
**Statement IV is true.**

### Final Summary
- **Statement I**: True
- **Statement II**: False
- **Statement III**: True
- **Statement IV**: True

The correct code about the complex is **I, III, and IV**.