Arrange the following in decreasing order of their stability :- `(I) CH_(3)-overset(oplus)(CH_(2)) " "(II) CH_(3)-underset(CH_(3))underset(|)overset(oplus)(CH)`
`(III) CH_(3)-underset(oplus)overset(CH_(3))overset(|)(C)-CH_(3) " "(IV) {:(CH_(2)-overset(o+)(C)H_(2)),(|),(F):}`

Options

A. `(a)II gt I gt III gt IV`
B. (b)`IV gt I gt II gt III`
C. (c)`IV gt III gt II gt I`
D. (d)`III gt II gt I gt IV`

Answer

To determine the stability of the given carbocations, we need to analyze the structure of each carbocation and the effects of substituents on the positive charge. The general rule is that the more alkyl groups attached to the positively charged carbon, the more stable the carbocation is due to the +I (inductive) effect, which helps to disperse the positive charge.

### Step-by-Step Solution:

1. **Identify the Carbocations**:
- (I) CH₃-CH₂⁺ (primary carbocation)
- (II) CH₃-CH(CH₃)⁺ (secondary carbocation)
- (III) CH₃-C(CH₃)₂⁺ (tertiary carbocation)
- (IV) CH₂⁺-CH₂-F (primary carbocation with a fluorine atom)

2. **Analyze Each Carbocation**:
- **(I)**: CH₃-CH₂⁺ has one alkyl group (methyl) donating electrons to stabilize the positive charge. This is a primary carbocation and is relatively unstable.
- **(II)**: CH₃-CH(CH₃)⁺ has two alkyl groups (one methyl and one ethyl) donating electrons, making it a secondary carbocation. This is more stable than the primary carbocation.
- **(III)**: CH₃-C(CH₃)₂⁺ has three alkyl groups (three methyl groups) donating electrons, making it a tertiary carbocation. This is the most stable due to maximum hyperconjugation and inductive effect.
- **(IV)**: CH₂⁺-CH₂-F has a fluorine atom, which is an electron-withdrawing group (-I effect). This makes the positive charge more pronounced and thus less stable compared to the others.

3. **Rank the Stability**:
- The most stable carbocation is (III) CH₃-C(CH₃)₂⁺ (tertiary).
- The next is (II) CH₃-CH(CH₃)⁺ (secondary).
- Then (I) CH₃-CH₂⁺ (primary).
- The least stable is (IV) CH₂⁺-CH₂-F due to the electron-withdrawing effect of fluorine.

### Final Order of Stability:
**(III) > (II) > (I) > (IV)**