Which of the following has an asymmetric carbon atom ?
(a)`CH_3 - CH_2 -CH_2Br`
(b)`CH_3 - underset(Br) underset(|) overset(H) overset(|)C- underset(CH_3) underset(|) CH - CH_3`
(c)`CH_3 - cH_2 -underset(CH_3)underset(|) overset(Br) overset(|)C-CH_3`
(d)`CH_3 - underset(Br) underset(|) overset(|) overset(CH_3) overset(|) C- CH_2 -CH_2-CH_3`

Options

A. `CH_3 - CH_2 -CH_2Br`
B. `CH_3 - underset(Br) underset(|) overset(H) overset(|)C- underset(CH_3) underset(|) CH - CH_3`
C. `CH_3 - cH_2 -underset(CH_3)underset(|) overset(Br) overset(|)C-CH_3`
D. `CH_3 - underset(Br) underset(|) overset(|) overset(CH_3) overset(|) C- CH_2 -CH_2-CH_3`

Explanation

To determine which of the given compounds has an asymmetric carbon atom, we need to identify a carbon atom that is bonded to four different substituents. An asymmetric carbon atom, also known as a chiral carbon, has no plane of symmetry and is typically responsible for optical activity in organic compounds.

Let's analyze each option step by step:

### Step 1: Analyze Option (a) `CH_3 - CH_2 - CH_2Br`
- The structure can be represented as:
```
H H Br
| | |
H - C - C - C
| |
H H
```
- The carbon atoms in this compound are:
- The first carbon (attached to 3 hydrogens and 1 carbon) - not asymmetric.
- The second carbon (attached to 2 hydrogens, 1 carbon, and 1 carbon) - not asymmetric.
- The third carbon (attached to 1 hydrogen, 1 carbon, and 1 bromine) - not asymmetric.

**Conclusion**: No asymmetric carbon in option (a).

### Step 2: Analyze Option (b) `CH_3 - Br - C - CH_3`
- The structure can be represented as:
```
CH3
|
Br - C
|
CH3
```
- The carbon atom in the center is bonded to:
- One bromine (Br)
- One methyl group (CH3)
- One hydrogen (H)
- One other carbon (CH3)

**Conclusion**: The central carbon is asymmetric because it is attached to four different groups (Br, CH3, H, and CH3). Thus, option (b) has an asymmetric carbon atom.

### Step 3: Analyze Option (c) `CH_3 - CH_2 - C(CH_3) - CH_3`
- The structure can be represented as:
```
CH3
|
C - CH3
|
CH2
|
CH3
```
- The central carbon is bonded to:
- Two methyl groups (CH3)
- One hydrogen (H)
- One carbon (CH2)

**Conclusion**: The central carbon is not asymmetric because it has two identical methyl groups.

### Step 4: Analyze Option (d) `CH_3 - Br - C - CH_2 - CH_2 - CH_3`
- The structure can be represented as:
```
CH3
|
Br - C
|
CH2
|
CH2
|
CH3
```
- The central carbon is bonded to:
- One bromine (Br)
- One hydrogen (H)
- One CH2 group
- One CH3 group

**Conclusion**: The central carbon is not asymmetric because it has two identical hydrogen atoms.

### Final Conclusion:
Only option (b) has an asymmetric carbon atom.

**Correct Answer**: (b) `CH_3 - Br - C - CH_3`