The decreasing order of stability of the carbonium ions
`C_(6)H_(5)CH_(2)^(+) (I), p-(CH_(3)O)C_(6)H_(4)CH_(2)^(+) (II)`
` p-(NO_(2))C_(6)H_(4)CH_(2)^(+) (III), p-(CH_(3))C_(6)H_(4)CH_(2)^(+) (IV)` is

Options

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

Explanation

To determine the decreasing order of stability of the given carbonium ions (carbocations), we need to analyze the effects of substituents on the stability of these ions. The stability of carbocations is influenced by the presence of electron-donating or electron-withdrawing groups.

### Step-by-Step Solution:

1. **Identify the Carbocations**:
- (I) C₆H₅CH₂⁺ (Benzyl cation)
- (II) p-(CH₃O)C₆H₄CH₂⁺ (Para-methoxybenzyl cation)
- (III) p-(NO₂)C₆H₄CH₂⁺ (Para-nitrobenzyl cation)
- (IV) p-(CH₃)C₆H₄CH₂⁺ (Para-methylbenzyl cation)

2. **Analyze the Effects of Substituents**:
- **(I) Benzyl cation (C₆H₅CH₂⁺)**: The phenyl group can stabilize the positive charge through resonance, making this carbocation relatively stable.
- **(II) Para-methoxybenzyl cation (p-(CH₃O)C₆H₄CH₂⁺)**: The methoxy group (-OCH₃) is an electron-donating group through resonance, which stabilizes the positive charge even more than the phenyl group alone.
- **(III) Para-nitrobenzyl cation (p-(NO₂)C₆H₄CH₂⁺)**: The nitro group (-NO₂) is an electron-withdrawing group, which destabilizes the positive charge, making this carbocation less stable.
- **(IV) Para-methylbenzyl cation (p-(CH₃)C₆H₄CH₂⁺)**: The methyl group (-CH₃) is a weak electron-donating group through hyperconjugation, providing some stability but not as much as the methoxy group.

3. **Rank the Stability**:
- The most stable carbocation is (II) p-(CH₃O)C₆H₄CH₂⁺ due to strong resonance stabilization.
- Next is (I) C₆H₅CH₂⁺, which has resonance stabilization from the phenyl group.
- Then (IV) p-(CH₃)C₆H₄CH₂⁺, which has some stabilization from hyperconjugation.
- Finally, (III) p-(NO₂)C₆H₄CH₂⁺ is the least stable due to the electron-withdrawing effect of the nitro group.

### Final Order of Stability:
The decreasing order of stability of the carbonium ions is:
**II > I > IV > III**