The correct order of dipole moment is :

Options

A. `CH_(4)gtNF_(3)gtNH_(3)gtH_(2)O`
B. `NF_(3)gtCH_(4)gtNH_(3)gtH_(2)O`
C. `NH_(3)gtNF_(3)gtCH_(4)gtH_(2)O`
D. `H_(2)OgtNH_(3)gtNF_(3)gtCH_(4)`

Answer

To determine the correct order of dipole moments for the given compounds (CH4, NF3, NH3, and H2O), we need to analyze the molecular structures and the electronegativities of the atoms involved. Here’s a step-by-step solution:

### Step 1: Identify the Structures
- **Methane (CH4)**: Tetrahedral structure with carbon at the center and four hydrogen atoms. The dipoles from C-H bonds cancel each other out due to symmetry.
- **Nitrogen trifluoride (NF3)**: Trigonal pyramidal structure with nitrogen at the center and three fluorine atoms. The dipole moments do not cancel out completely due to the presence of a lone pair on nitrogen.
- **Ammonia (NH3)**: Also a trigonal pyramidal structure with nitrogen at the center and three hydrogen atoms. The dipole moments do not cancel out completely due to the presence of a lone pair on nitrogen.
- **Water (H2O)**: Bent structure with oxygen at the center and two hydrogen atoms. The dipole moments do not cancel out due to the bent shape and the high electronegativity of oxygen.

### Step 2: Analyze Electronegativity
- **Electronegativity Values**:
- Carbon (C): 2.5
- Hydrogen (H): 2.1
- Nitrogen (N): 3.0
- Oxygen (O): 3.5
- Fluorine (F): 4.0

### Step 3: Determine Dipole Moments
- **CH4**: The dipole moment is effectively zero due to symmetry.
- **NF3**: The dipole moment is directed towards fluorine, but the lone pair on nitrogen reduces the overall dipole moment.
- **NH3**: The dipole moment is directed towards nitrogen, and the lone pair contributes to a significant dipole moment.
- **H2O**: The dipole moment is directed towards oxygen, and due to its bent shape and high electronegativity, it has a significant dipole moment.

### Step 4: Compare the Dipole Moments
- **Order of Dipole Moments**:
- H2O > NH3 > NF3 > CH4

### Final Answer
The correct order of dipole moments is: **H2O > NH3 > NF3 > CH4**.

---