The decreasing order of dipole moment of the folliwng is:
I. `CH_(3)Cl`, II. `CH_(3)Br`, III. `CH_(3)F`

Options

A. `(I) gt (II) gt (III)`
B. `(I) gt (III) gt (II)`
C. `(II) gt (I) gt (III)`
D. `(II) gt (III) gt (I)`

Explanation

To determine the decreasing order of dipole moment for the alkyl halides \(CH_3Cl\), \(CH_3Br\), and \(CH_3F\), we need to consider two main factors: bond length and electronegativity difference between carbon and the halogen atoms.

### Step-by-Step Solution:

1. **Identify the Halogens and Their Electronegativity:**
- The halogens involved are chlorine (Cl), bromine (Br), and fluorine (F).
- Their electronegativities (according to the Pauling scale) are approximately:
- Fluorine (F): 4.0
- Chlorine (Cl): 3.0
- Bromine (Br): 2.8

2. **Determine the Bond Lengths:**
- The bond lengths for the carbon-halogen bonds are as follows:
- \(C-F\) bond is the shortest (strongest bond).
- \(C-Cl\) bond is longer than \(C-F\).
- \(C-Br\) bond is the longest (weakest bond).

3. **Analyze the Dipole Moment:**
- The dipole moment (\(\mu\)) is influenced by both the bond length and the electronegativity difference. The formula for dipole moment is given by:
\[ \mu = q \cdot r \]
where \(q\) is the charge difference (related to electronegativity) and \(r\) is the bond length.
- A larger electronegativity difference and longer bond length generally contribute to a higher dipole moment.

4. **Comparing the Dipole Moments:**
- For \(CH_3F\):
- High electronegativity difference (4.0 - 2.5 = 1.5) and short bond length.
- For \(CH_3Cl\):
- Moderate electronegativity difference (3.0 - 2.5 = 0.5) and moderate bond length.
- For \(CH_3Br\):
- Lowest electronegativity difference (2.8 - 2.5 = 0.3) and longest bond length.

5. **Order of Dipole Moment:**
- Based on the analysis:
- \(CH_3Cl\) has the highest dipole moment due to a balance of moderate bond length and electronegativity difference.
- \(CH_3F\) has a high dipole moment due to a significant electronegativity difference but a very short bond length.
- \(CH_3Br\) has the lowest dipole moment due to the least electronegativity difference and longest bond length.
- Therefore, the decreasing order of dipole moment is:
\[ CH_3Cl > CH_3F > CH_3Br \]

### Final Answer:
The decreasing order of dipole moment is:
1. \(CH_3Cl\)
2. \(CH_3F\)
3. \(CH_3Br\)