If a compound has `n` asymmetric carbon atoms with different terminal groups, the number of stereoisomers is given by the formula:

Options

A. `(1//2)^(n)`
B. `2^(n)`
C. `2sqrt(n)`
D. `sqrt(2)n`

Answer

To determine the number of stereoisomers for a compound with `n` asymmetric carbon atoms that have different terminal groups, we can follow these steps:

### Step-by-Step Solution:

1. **Identify Asymmetric Carbon Atoms**:
- An asymmetric carbon atom (also known as a chiral center) is a carbon atom that is attached to four different groups.
- For our calculation, we need to count how many such asymmetric carbon atoms (n) are present in the compound.

2. **Understanding Terminal Groups**:
- Terminal groups refer to the groups attached to the ends of the carbon chain. In this case, we are told that these terminal groups are different for each asymmetric carbon atom.

3. **Apply the Formula**:
- The formula to calculate the number of stereoisomers when there are `n` asymmetric carbon atoms is given by:
\[ \text{Number of Stereoisomers} = 2^n \]
- This formula arises because each asymmetric carbon can exist in two configurations (R or S), leading to a total of \(2^n\) combinations for `n` asymmetric carbons.

4. **Example Calculation**:
- If we have a compound with 4 asymmetric carbon atoms (n = 4), we can substitute this value into the formula:
\[ \text{Number of Stereoisomers} = 2^4 = 16 \]
- Thus, for 4 asymmetric carbon atoms with different terminal groups, there would be 16 stereoisomers.

5. **Conclusion**:
- Therefore, the correct answer to the question is that the number of stereoisomers for a compound with `n` asymmetric carbon atoms with different terminal groups is given by \(2^n\).

### Final Answer:
The number of stereoisomers is given by the formula \(2^n\).