The order of stability of the alkenes
`underset(I)(R_(2)C=CR_(2)') underset(II)(R_(2)C=CHR), underset(III)(R_(2)C=CH_(2)')underset(IV)
(RCH=CHR,) "and" underset(V)(RCH=CH_(2))`
is -

Options

A. `IgtIIgtIIIgtIVgtV`
B. `I=IIgtIIIgtIVgtV`
C. `IIgtIIgtIVgtIIIgtV`
D. `VgtIVgtIIIgtIgtII`

Answer

To determine the order of stability of the given alkenes based on the number of alpha hydrogens and hyperconjugation, we will analyze each alkene step by step.

### Step-by-Step Solution:

1. **Identify the Structures of the Alkenes**:
- Alkene I: \( R_2C=CR_2' \)
- Alkene II: \( R_2C=CHR \)
- Alkene III: \( R_2C=CH_2 \)
- Alkene IV: \( RCH=CHR \)
- Alkene V: \( RCH=CH_2 \)

2. **Assume R as Methyl (CH₃)**:
To simplify the calculation, we will assume that R is a methyl group (CH₃) for each alkene.

3. **Count Alpha Hydrogens**:
- **Alkene I**: \( R_2C=CR_2' \) (Assuming R = CH₃)
- Structure: \( (CH_3)_{2}C=CH_{2} \)
- Alpha Hydrogens: 12 (from both \( CH_3 \) groups)

- **Alkene II**: \( R_2C=CHR \)
- Structure: \( (CH_3)_{2}C=CH_{3} \)
- Alpha Hydrogens: 9 (from two \( CH_3 \) groups and one \( CH \) group)

- **Alkene III**: \( R_2C=CH_2 \)
- Structure: \( (CH_3)_{2}C=CH_{2} \)
- Alpha Hydrogens: 6 (from two \( CH_3 \) groups)

- **Alkene IV**: \( RCH=CHR \)
- Structure: \( CH_3CH=CH_{3} \)
- Alpha Hydrogens: 6 (from two \( CH_3 \) groups)

- **Alkene V**: \( RCH=CH_2 \)
- Structure: \( CH_3CH=CH_{2} \)
- Alpha Hydrogens: 3 (from one \( CH_3 \) group)

4. **Order of Stability**:
Based on the number of alpha hydrogens:
- Alkene I: 12 alpha hydrogens (most stable)
- Alkene II: 9 alpha hydrogens
- Alkene III: 6 alpha hydrogens
- Alkene IV: 6 alpha hydrogens
- Alkene V: 3 alpha hydrogens (least stable)

5. **Final Order**:
The order of stability from most stable to least stable is:
- I > II > III = IV > V

### Conclusion:
Thus, the order of stability of the alkenes is:
**I > II > III = IV > V**