The correct order of dipole moment is :

Options

A. `CH_(4) lt NF_(3) lt NH_(3)ltH_(2)O`
B. `NF_(3) ltCH_(4) ltNH_(3) ltH_(2)O`
C. `NH_(3) ltNF_(3) ltCH_(4) ltH_(2)O`
D. `H_(2)O lt NH_(3) lt NF_(3) lt CH_(4)`

Explanation

To determine the correct order of dipole moments for the given molecules (H2O, NH3, NF3, and CH4), we will analyze each molecule based on the electronegativity of their central atoms and their molecular geometry.

### Step-by-Step Solution:

1. **Understanding Dipole Moment**:
- Dipole moment (µ) is a measure of the separation of positive and negative charges in a molecule. It depends on the difference in electronegativity between the atoms and the geometry of the molecule.

2. **Identifying the Molecules**:
- The molecules we need to analyze are:
- H2O (Water)
- NH3 (Ammonia)
- NF3 (Nitrogen trifluoride)
- CH4 (Methane)

3. **Electronegativity Values**:
- The electronegativity values (Pauling scale) for the relevant atoms are approximately:
- O (Oxygen) = 3.44
- N (Nitrogen) = 3.04
- F (Fluorine) = 3.98
- C (Carbon) = 2.55
- Higher electronegativity indicates a stronger ability to attract electrons.

4. **Analyzing Each Molecule**:
- **H2O**:
- Oxygen is highly electronegative, and the molecule has a bent shape due to the two lone pairs on oxygen. This results in a significant dipole moment directed towards the oxygen.
- **NH3**:
- Nitrogen is less electronegative than oxygen but still significant. The pyramidal shape allows the dipole moments from the N-H bonds to add up, resulting in a net dipole moment directed towards nitrogen.
- **NF3**:
- Although fluorine is highly electronegative, the shape of NF3 is trigonal pyramidal. The dipole moments from the N-F bonds partially cancel due to the lone pair on nitrogen, resulting in a lower net dipole moment compared to NH3.
- **CH4**:
- Methane has a tetrahedral shape and is symmetric. The dipole moments from the C-H bonds cancel each other out, resulting in a net dipole moment of zero.

5. **Comparing Dipole Moments**:
- Based on the analysis:
- H2O has the highest dipole moment due to its bent shape and high electronegativity of oxygen.
- NH3 has a lower dipole moment than H2O but higher than NF3 due to the supporting dipole contributions from the N-H bonds.
- NF3 has a lower dipole moment than NH3 because of the partial cancellation of dipole moments.
- CH4 has no dipole moment due to its symmetrical structure.

6. **Final Order of Dipole Moments**:
- The correct order of dipole moments is:
- H2O > NH3 > NF3 > CH4

### Conclusion:
The correct order of dipole moments is:
**H2O > NH3 > NF3 > CH4**