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 likabe isomerism
`(IV)` It shows coordination isomerism`

Options

A. `III,IV`
B. `I,III` and `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: Analyze the IUPAC Name
The first statement claims that the IUPAC name of the compound is "pentaamminenitrito-N-chromium(III) tetrachlorozincate(II)".

- The complex cation is `[Cr(NO2)(NH3)5]`. Here, there are five ammonia (NH3) ligands and one nitrito (NO2) ligand. The nitrito ligand is bonded through the nitrogen atom (hence "nitrito-N").
- The oxidation state of chromium (Cr) in this complex can be determined as follows: Each NH3 is neutral (0 charge), and NO2 contributes -1 charge (as nitrito-N). Therefore, to balance the overall charge of the cation to +3 (for Cr(III)), Cr must be in the +3 oxidation state.
- The anionic part is `[ZnCl4]`, where zinc (Zn) is in the +2 oxidation state (as each chloride ion, Cl, has a -1 charge and there are four of them).
- Therefore, the complete IUPAC name is indeed "pentaamminenitrito-N-chromium(III) tetrachlorozincate(II)".

**Conclusion for Step 1**: The first statement is **correct**.

### Step 2: Check for Geometrical Isomerism
The second statement claims that the complex shows geometrical isomerism.

- Geometrical isomerism occurs in coordination complexes when there are different spatial arrangements of ligands around the central metal atom.
- In this case, the cation `[Cr(NO2)(NH3)5]` has a coordination number of 6 (5 NH3 and 1 NO2). However, with only one nitrito ligand, there is only one possible arrangement (the nitrito ligand can only occupy one position).
- For geometrical isomerism to occur, there must be at least two pairs of ligands in different positions (like trans or cis arrangements). Since there is only one nitrito ligand, it cannot create geometrical isomers.

**Conclusion for Step 2**: The second statement is **incorrect**.

### Step 3: Check for Linkage Isomerism
The third statement claims that the complex shows linkage isomerism.

- Linkage isomerism occurs when a ligand can coordinate to the metal in more than one way. In this case, the nitrito ligand (NO2-) can bind through either the nitrogen atom (N) or the oxygen atom (O).
- Therefore, the complex can exist in two forms: one where nitrito is bonded through nitrogen (nitrito-N) and another where it is bonded through oxygen (nitrito-O).

**Conclusion for Step 3**: The third statement is **correct**.

### Step 4: Check for Coordination Isomerism
The fourth statement claims that the complex shows coordination isomerism.

- Coordination isomerism occurs when the composition of the coordination sphere changes. In this complex, we have two metal centers: chromium in the cation and zinc in the anion.
- The ligands can exchange between the cationic and anionic parts of the complex. For example, ligands from the zinc complex can swap with those from the chromium complex, leading to different isomers.

**Conclusion for Step 4**: The fourth statement is **correct**.

### Final Conclusion
Based on the analysis:
- Statement (I) is correct.
- Statement (II) is incorrect.
- Statement (III) is correct.
- Statement (IV) is correct.

Thus, the correct codes about the complex `[Cr(NO_(2))(NH_(3))_(5)][ZnCl_(4)]` are **(I), (III), and (IV)**.