The bond dissociation energies of the following
`underset(I)(CH_(3)-H)` `underset(II)(CH_(3)CH_(2)-H)` `underset(III)(CH_(2)=CH-CH_(2)-H)` `underset(IV)(C_(6)H_(5)-H)`
vary in the order :

Options

A. `IgtIIgtIIIgtIV`
B. `IVgtIIIgtIIgtI`
C. `IVgtIgtIIgtIII`
D. `IIgtIgtIVgtIII`

Answer

To determine the order of bond dissociation energies for the given compounds, we need to analyze the stability of the radicals formed when the respective C-H bonds are cleaved. The compounds in question are:

1. **(I) CH₃-H** (Methyl radical)
2. **(II) CH₃CH₂-H** (Ethyl radical)
3. **(III) CH₂=CH-CH₂-H** (Allyl radical)
4. **(IV) C₆H₅-H** (Phenyl radical)

### Step-by-Step Solution:

1. **Identify the Radicals Formed**:
- For **(I)** CH₃-H, cleaving the bond forms a methyl radical (CH₃•).
- For **(II)** CH₃CH₂-H, cleaving the bond forms an ethyl radical (CH₃CH₂•).
- For **(III)** CH₂=CH-CH₂-H, cleaving the bond forms an allyl radical (CH₂=CH-CH₂•).
- For **(IV)** C₆H₅-H, cleaving the bond forms a phenyl radical (C₆H₅•).

2. **Assess the Stability of the Radicals**:
- **Methyl Radical (CH₃•)**: This is a primary radical and is the least stable.
- **Ethyl Radical (CH₃CH₂•)**: This is a primary radical as well, but slightly more stable than the methyl radical due to the presence of an additional carbon.
- **Allyl Radical (CH₂=CH-CH₂•)**: This radical is stabilized by resonance, making it more stable than both methyl and ethyl radicals.
- **Phenyl Radical (C₆H₅•)**: This radical is also stabilized by resonance, but it is less stable than the allyl radical due to the nature of the resonance in the benzene ring.

3. **Order of Bond Dissociation Energies**:
- The bond dissociation energy is inversely related to the stability of the radical formed. The more stable the radical, the lower the bond dissociation energy.
- Therefore, the order of bond dissociation energies from highest to lowest is:
- **(IV) C₆H₅-H** (highest)
- **(I) CH₃-H**
- **(II) CH₃CH₂-H**
- **(III) CH₂=CH-CH₂-H** (lowest)

### Final Order:
The bond dissociation energies vary in the order:
**(IV) > (I) > (II) > (III)**