`Ni^(+2)` form a complex inon in water having the formula `[Ni(H_(2)O)_(6)]^(+2)`. How many of the following statement are true for the complex ion ?
(i) The complex is octahedral in shape (ii) The complex is diamagnetic in nature .
(iii) `Ni^(+2)` has incompletely filled 3d subshell. (iv). Secodary valency of `Ni^(+2)` is 6
(v) All the bonds (metal-ligand ) are perpendicular to each other. (vi) All the 3d orbitals of `Ni^(+2)` are degenerate
(vii) Total spin of the complex is 1. (viii) The hybridisation of `Ni^(+2) is d^(2)sp^(3)`
(ix) The complex is more stable than `[Ni(en)_(3)]^(+2)` (x) Effective atomic number of `Ni^(+2)` is 36.

Answer

To determine how many of the statements about the complex ion \([Ni(H_2O)_6]^{+2}\) are true, we will analyze each statement step by step.

### Step-by-Step Solution:

1. **Statement (i): The complex is octahedral in shape.**
- The coordination number of \([Ni(H_2O)_6]^{+2}\) is 6, which typically results in an octahedral geometry.
- **Conclusion:** True.

2. **Statement (ii): The complex is diamagnetic in nature.**
- The electronic configuration of \(Ni^{+2}\) is \(3d^8\). In an octahedral field, the \(d\) orbitals split into two sets. Filling the \(d\) orbitals will result in 2 unpaired electrons.
- **Conclusion:** False (the complex is paramagnetic).

3. **Statement (iii): \(Ni^{+2}\) has an incompletely filled 3d subshell.**
- As noted, \(Ni^{+2}\) has the configuration \(3d^8\), which is indeed incompletely filled.
- **Conclusion:** True.

4. **Statement (iv): The secondary valency of \(Ni^{+2}\) is 6.**
- The secondary valency corresponds to the coordination number, which is 6 in this case.
- **Conclusion:** True.

5. **Statement (v): All the bonds (metal-ligand) are perpendicular to each other.**
- In an octahedral complex, the ligand bonds are not perpendicular to each other; they are at 90 degrees to each other in pairs.
- **Conclusion:** False.

6. **Statement (vi): All the 3d orbitals of \(Ni^{+2}\) are degenerate.**
- In an octahedral field, the \(d\) orbitals split into two sets (t2g and eg), so they are not degenerate.
- **Conclusion:** False.

7. **Statement (vii): Total spin of the complex is 1.**
- With 2 unpaired electrons, the total spin \(S\) is calculated as \(S = \frac{n}{2}\), where \(n\) is the number of unpaired electrons. Here, \(S = \frac{2}{2} = 1\).
- **Conclusion:** True.

8. **Statement (viii): The hybridization of \(Ni^{+2}\) is \(d^2sp^3\).**
- The correct hybridization for a coordination number of 6 is \(sp^3d^2\).
- **Conclusion:** False.

9. **Statement (ix): The complex is more stable than \([Ni(en)_3]^{+2}\).**
- Ethylenediamine (en) is a bidentate ligand, which typically forms more stable complexes due to chelation. Thus, \([Ni(en)_3]^{+2}\) is more stable than \([Ni(H_2O)_6]^{+2}\).
- **Conclusion:** False.

10. **Statement (x): Effective atomic number of \(Ni^{+2}\) is 36.**
- The effective atomic number (EAN) is calculated as:
\[ EAN = Z - n + 2L \]
where \(Z\) is the atomic number (28 for Ni), \(n\) is the charge (+2), and \(L\) is the number of ligands (6). Thus,
\[ EAN = 28 - 2 + 12 = 38. \]
- **Conclusion:** False.

### Summary of True Statements:
- True Statements: (i), (iii), (iv), (vii)
- Total True Statements: 4

### Final Answer:
The total number of true statements is **4**.