Total number of possible isomers (both structural as well as stereoisomers) of cyclic ethers of molecular formula C₄H₈O is:

The correct option is 10.

To determine the total number of cyclic ether isomers for the molecular formula $C_4{H}_{8}O$ (including both structural and stereoisomers), we can proceed step-by-step as follows:

Step 1: Calculate the Degree of Unsaturation (Double Bond Equivalent, DBE)
The formula for DBE is:

$\text{DBE}=C+1-\frac{H}{2}$

For $C_4{H}_{8}O$:

$\text{DBE}=4+1-\frac{8}{2}=1$

Since the isomers must be cyclic ethers, the ring accounts for the 1 degree of unsaturation. Therefore, the molecules will contain a single ring with no double bonds.

Step 2: Classify by Ring Size
We can have cyclic ethers with 5-membered, 4-membered, and 3-membered rings containing oxygen.

1. 5-Membered Ring (Oxolane / Tetrahydrofuran ring)
A 5-membered ring consists of 4 carbon atoms and 1 oxygen atom.

• Tetrahydrofuran (THF): There are no substituents, and no chiral centers. This gives 1 isomer.

2. 4-Membered Ring (Oxetane ring)
A 4-membered ring consists of 3 carbon atoms and 1 oxygen atom. The remaining 1 carbon atom is present as a methyl substituent.

• 2-Methyloxetane: The methyl group is at carbon position 2. This carbon is chiral because it is bonded to -H, -CH₃, -O-CH₂-, and -CH₂-CH₂-. This gives a pair of enantiomers:
  • (R)-2-methyloxetane
  • (S)-2-methyloxetane
  This contributes 2 isomers.
• 3-Methyloxetane: The methyl group is at carbon position 3. Carbon-3 is symmetric (not chiral). This contributes 1 isomer.

Total for 4-membered rings = 3 isomers.

3. 3-Membered Ring (Oxirane / Epoxide ring)
A 3-membered ring consists of 2 carbon atoms and 1 oxygen atom. The remaining 2 carbon atoms can be attached in two ways:

• Case A: One ethyl substituent
  • Ethyloxirane: The carbon attached to the ethyl group is chiral. This gives a pair of enantiomers:
    - (R)-ethyloxirane
    - (S)-ethyloxirane
  This contributes 2 isomers.
• Case B: Two methyl substituents
  • 2,2-Dimethyloxirane: Both methyl groups are attached to the same ring carbon. There are no chiral centers. This contributes 1 isomer.
  • 2,3-Dimethyloxirane: Each ring carbon has one methyl group. Both ring carbons are chiral centers:
    - cis-2,3-dimethyloxirane (meso compound, optically inactive due to internal symmetry): 1 isomer.
    - trans-2,3-dimethyloxirane (chiral, exists as a pair of enantiomers, (2R,3R) and (2S,3S)): 2 isomers.

Total for 3-membered rings = 2 (ethyloxirane) + 1 (2,2-dimethyloxirane) + 3 (2,3-dimethyloxirane) = 6 isomers.

Step 3: Total Count
Adding up all the structural and stereoisomers:
$\text{Total}=1\text{ (5-membered)}+3\text{ (4-membered)}+6\text{ (3-membered)}=10$