Step 1: Understanding the dipole moment.
The dipole moment of a molecule is influenced by the electronegativity difference between atoms, the molecular shape, and the presence of any polar bonds. A greater electronegativity difference between atoms, particularly in the case of the halogens and oxygen, leads to a greater dipole moment.
Step 2: Analyzing the compounds.
- Fluoromethane has the highest dipole moment because fluorine is the most electronegative element, creating a strong dipole.
- Chloromethane has a slightly lower dipole moment than fluoromethane because chlorine is less electronegative than fluorine.
- Methanol has a significant dipole moment due to the highly polar O-H bond, but the dipole moment is less than that of fluoromethane and chloromethane because the C-H bonds are not polar enough to add much to the dipole moment.
- Dimethylether has the smallest dipole moment because the two C-O bonds cancel each other out, and it has no highly electronegative atoms like fluorine or chlorine.
Step 3: Conclusion.
The correct order of the dipole moments is: chloromethane>fluoromethane>methanol>dimethylether.
Final Answer:
\[
\boxed{\text{chloromethane>fluoromethane>methanol>dimethylether}}
\]