Arrange the following compounds in order of their reactivity towards `S_N2` reaction
(i) `CH_3(CH_2)_3CH_2Br`
(ii) `(CH_3)_2CHCH_2CH_2Br`
(iii) `CH_(3)CH_(2)-overset(CH_(3))overset("| ")"CH"-CH_(2)Br`
(iv) `CH_(3)CH_(2)-overset(CH_(3))overset("| ")"CH"-CH_(2)Br`

Options

A. `(i) gt (ii) gt (iii) gt (iv)`
B. `(ii) gt (iii) gt (iv) gt (i) `
C. `(iii) gt (i) gt (ii) gt (iv)`
D. `(iv ) gt (ii) gt (i) gt (iii) `

Answer

To determine the reactivity of the given compounds towards an `S_N2` reaction, we need to analyze the structure of each compound and the steric hindrance around the carbon atom that is bonded to the bromine (Br) atom. The `S_N2` mechanism is characterized by a backside attack of the nucleophile, which is more favorable when there is less steric hindrance.

### Step-by-Step Solution:

1. **Identify the Structure of Each Compound:**
- (i) `CH_3(CH_2)_3CH_2Br` - This is a primary alkyl halide.
- (ii) `(CH_3)_2CHCH_2CH_2Br` - This is also a primary alkyl halide.
- (iii) `CH_3CH_2-overset{CH_3}{|}CH-CH_2Br` - This is a secondary alkyl halide.
- (iv) `CH_3CH_2-overset{CH_3}{|}CH-CH_2Br` - This is also a secondary alkyl halide.

2. **Determine the Type of Each Alkyl Halide:**
- Primary alkyl halides are less hindered and more reactive in `S_N2` reactions compared to secondary alkyl halides.
- The first two compounds (i) and (ii) are primary, while (iii) and (iv) are secondary.

3. **Analyze Steric Hindrance:**
- For compound (i) `CH_3(CH_2)_3CH_2Br`, there is minimal steric hindrance, making it very reactive.
- For compound (ii) `(CH_3)_2CHCH_2CH_2Br`, the hindrance is slightly more due to the presence of two methyl groups, but it is still a primary halide, thus reactive.
- For compounds (iii) and (iv), both are secondary halides, but we need to compare their steric hindrance. The positioning of the methyl groups affects the reactivity.
- In (iii), the methyl groups are further away from the carbon attached to Br compared to (iv), which has the methyl groups closer to the carbon attached to Br, leading to more hindrance.

4. **Order of Reactivity:**
- The order of reactivity towards `S_N2` reactions will be:
1. (i) `CH_3(CH_2)_3CH_2Br` (most reactive)
2. (ii) `(CH_3)_2CHCH_2CH_2Br`
3. (iii) `CH_3CH_2-overset{CH_3}{|}CH-CH_2Br`
4. (iv) `CH_3CH_2-overset{CH_3}{|}CH-CH_2Br` (least reactive)

### Final Order:
The final order of reactivity towards `S_N2` reaction is:
1. (i) > 2. (ii) > 3. (iii) > 4. (iv)