Rank of the following groups in order of R,S precedence (IV is highest) :
`{:(-CH(CH_(3))_(2),-CH_(2)CH_(2)Br,-CH_(2)Br,-C(CH_(3))_(3)),(1,2,3,4):}`

Options

A. `{:(I,II,III,IV),(3,2,4,1):}`
B. `{:(I,II,III),(1,4,2):}`
C. `{:(I,II,III,IV),(1,4,2,2):}`
D. `{:(I,II,III),(3,4,2):}`

Explanation

To rank the given groups according to R,S precedence using the Cahn-Ingold-Prelog (CIP) priority rules, we will follow these steps:

### Step 1: Identify the atoms directly attached to the chiral center in each group.
- **Group 1:** -CH(CH₃)₂ (This group has a carbon attached to two methyl groups and one hydrogen)
- **Group 2:** -CH₂CH₂Br (This group has a carbon attached to two hydrogens and one bromine)
- **Group 3:** -CH₂Br (This group has a carbon attached to one hydrogen and one bromine)
- **Group 4:** -C(CH₃)₃ (This group has a carbon attached to three methyl groups)

### Step 2: Determine the atomic number of the atoms directly attached to the chiral centers.
- **Group 1:** The first atom is carbon (C), which has an atomic number of 6.
- **Group 2:** The first atom is carbon (C), which has an atomic number of 6, and the second atom is bromine (Br), which has an atomic number of 35.
- **Group 3:** The first atom is carbon (C), which has an atomic number of 6, and the second atom is bromine (Br), which has an atomic number of 35.
- **Group 4:** The first atom is carbon (C), which has an atomic number of 6.

### Step 3: Compare the groups based on the atomic numbers of the atoms attached.
- **Group 1 (-CH(CH₃)₂):** The highest priority atom is carbon (C) with two methyl groups attached.
- **Group 2 (-CH₂CH₂Br):** The highest priority atom is bromine (Br) since it has a higher atomic number than hydrogen (H).
- **Group 3 (-CH₂Br):** The highest priority atom is bromine (Br) since it has a higher atomic number than hydrogen (H).
- **Group 4 (-C(CH₃)₃):** The highest priority atom is carbon (C) with three methyl groups attached.

### Step 4: Assign priorities based on the highest atomic numbers.
- **Group 1 (-CH(CH₃)₂):** Priority 3 (C with two CH₃)
- **Group 2 (-CH₂CH₂Br):** Priority 2 (C with Br)
- **Group 3 (-CH₂Br):** Priority 1 (C with Br)
- **Group 4 (-C(CH₃)₃):** Priority 4 (C with three CH₃)

### Final Ranking:
1. **Group 3 (-CH₂Br)** - Highest priority (1)
2. **Group 2 (-CH₂CH₂Br)** - Second priority (2)
3. **Group 1 (-CH(CH₃)₂)** - Third priority (3)
4. **Group 4 (-C(CH₃)₃)** - Lowest priority (4)

Thus, the final order of precedence is:
**-CH₂Br > -CH₂CH₂Br > -CH(CH₃)₂ > -C(CH₃)₃**