The denticity of the ligand `N(CH_(2)CH_(2)NH_(2))_(3)` is

Explanation

To determine the denticity of the ligand \( N(CH_2CH_2NH_2)_3 \), we will analyze its structure and identify the number of donor atoms that can coordinate with a metal ion.

### Step-by-Step Solution:

1. **Identify the Structure of the Ligand**:
The ligand \( N(CH_2CH_2NH_2)_3 \) consists of a central nitrogen atom bonded to three ethylene diamine groups (each containing an amino group, \( NH_2 \)).

2. **Identify the Donor Atoms**:
Each ethylene diamine group has two nitrogen atoms that can donate lone pairs to a metal ion. Since there are three such groups, we need to count the total number of nitrogen donor atoms.

3. **Count the Nitrogen Atoms**:
- Each of the three ethylene diamine groups contributes two nitrogen atoms.
- Therefore, the total number of nitrogen atoms is:
\[ 3 \text{ groups} \times 2 \text{ nitrogen atoms/group} = 6 \text{ nitrogen atoms} \]

4. **Determine the Denticity**:
The denticity of a ligand is defined as the number of donor atoms that can coordinate to a central metal ion. In this case, since there are 6 nitrogen atoms that can coordinate with the metal ion, the denticity of the ligand \( N(CH_2CH_2NH_2)_3 \) is 6.

### Final Answer:
The denticity of the ligand \( N(CH_2CH_2NH_2)_3 \) is **6**.