Rank the following free radicals in order of decreasing stability
`(I)C_(6)H_(5) " "overset(.)CHC_(6)H_(5)" "(II)C_(6)H_(5)- overset(.)CH - CH = CH_(2)`
`(III)CH_(3)-overset(.)CH - CH_(3)" "(IV) C_(6)H_(5)- overset(.)CH - CH_(3)`
`(V) CH_(3)CH " "CHCH_(2)overset(.)CH_(2)`
`(VI) CH_(3) - CH_(2) - underset(CH_(3))underset(|)overset(.)C-CH_(3)`

Options

A. `I gt II gt IV gt VI gt III gt V`
B. `VI gt V gt IV gt III gt II gt I`
C. `I gt II gt III gt IV gt V gt VI`
D. `I gt IV gt VI gt V gt II gt III`

Answer

To rank the given free radicals in order of decreasing stability, we will analyze each free radical based on two main factors: resonance and the inductive effect (plus I effect).

### Step-by-Step Solution:

1. **Identify the Free Radicals:**
- (I) \( C_6H_5 \cdot CHC_6H_5 \)
- (II) \( C_6H_5 \cdot CH - CH = CH_2 \)
- (III) \( CH_3 \cdot CH - CH_3 \)
- (IV) \( C_6H_5 \cdot CH - CH_3 \)
- (V) \( CH_3CH \cdot CHCH_2 \cdot CH_2 \)
- (VI) \( CH_3 - CH_2 - (CH_3) \cdot C - CH_3 \)

2. **Analyze Stability Based on Resonance:**
- **(I)**: The free radical is stabilized by resonance from two phenyl groups. This makes it highly stable.
- **(II)**: The free radical has resonance due to the phenyl group, but only one phenyl group is present, making it less stable than (I).
- **(III)**: The free radical has no resonance but is a secondary radical (2°), which is more stable than a primary radical.
- **(IV)**: This radical has resonance from the phenyl group and is also a secondary radical, making it more stable than (III).
- **(V)**: This is a primary radical (1°) with no resonance, making it less stable than (III) and (IV).
- **(VI)**: This is a tertiary radical (3°) with a strong inductive effect from three methyl groups, but no resonance, making it less stable than (I) and (II).

3. **Rank the Free Radicals:**
- Based on the analysis, we can rank the radicals in order of decreasing stability:
1. (I) \( C_6H_5 \cdot CHC_6H_5 \) - Most stable due to resonance from two phenyl groups.
2. (II) \( C_6H_5 \cdot CH - CH = CH_2 \) - Stable due to resonance from one phenyl group.
3. (IV) \( C_6H_5 \cdot CH - CH_3 \) - Stable due to resonance and being a secondary radical.
4. (III) \( CH_3 \cdot CH - CH_3 \) - Secondary radical but no resonance.
5. (VI) \( CH_3 - CH_2 - (CH_3) \cdot C - CH_3 \) - Tertiary radical but no resonance, but has a strong inductive effect.
6. (V) \( CH_3CH \cdot CHCH_2 \cdot CH_2 \) - Least stable as it is a primary radical with no resonance.

### Final Ranking:
1. (I)
2. (II)
3. (IV)
4. (III)
5. (VI)
6. (V)