A DNA molecule in which both strands have radioactive thymidine is allowed to duplicate in an environment containing non- radioactive thymidine. What will be the exact number of DNA molecules that contains the radio active thymidine after 3 duplications -

Options

A. One
B. Two
C. Four
D. Eight

Answer

To solve the problem, we need to understand how DNA replication works, especially in the context of radioactive and non-radioactive thymidine. The key points to consider are:

1. **Semi-Conservative Replication**: DNA replication is semi-conservative, meaning each new DNA molecule consists of one old (template) strand and one new strand.

2. **Initial Condition**: We start with one DNA molecule where both strands contain radioactive thymidine.

3. **Environment**: The environment contains non-radioactive thymidine, which will be incorporated into the new strands during replication.

Now, let's go through the steps of replication over three duplications:

### Step 1: First Duplication
- **Initial DNA Molecule**: 1 molecule (both strands are radioactive).
- **After Replication**: Each strand serves as a template.
- **Result**: 2 DNA molecules are formed.
- 1st DNA molecule: 1 radioactive strand (from the original) + 1 non-radioactive strand (newly synthesized).
- 2nd DNA molecule: 1 radioactive strand (from the original) + 1 non-radioactive strand (newly synthesized).

**Total radioactive DNA molecules after 1st duplication**: 2

### Step 2: Second Duplication
- **Starting with**: 2 DNA molecules (each with 1 radioactive and 1 non-radioactive strand).
- **After Replication**: Each of these 2 molecules will replicate.
- **Result**: 4 DNA molecules are formed.
- 1st DNA molecule: 1 radioactive + 1 non-radioactive (from the first molecule).
- 2nd DNA molecule: 1 radioactive + 1 non-radioactive (from the first molecule).
- 3rd DNA molecule: 1 radioactive + 1 non-radioactive (from the second molecule).
- 4th DNA molecule: 1 radioactive + 1 non-radioactive (from the second molecule).

**Total radioactive DNA molecules after 2nd duplication**: 4 (2 from each of the original 2)

### Step 3: Third Duplication
- **Starting with**: 4 DNA molecules (each with 1 radioactive and 1 non-radioactive strand).
- **After Replication**: Each of these 4 molecules will replicate.
- **Result**: 8 DNA molecules are formed.
- Each of the 4 molecules will produce 2 new molecules, leading to:
- 1st DNA molecule: 1 radioactive + 1 non-radioactive.
- 2nd DNA molecule: 1 radioactive + 1 non-radioactive.
- 3rd DNA molecule: 1 radioactive + 1 non-radioactive.
- 4th DNA molecule: 1 radioactive + 1 non-radioactive.
- 5th DNA molecule: 1 radioactive + 1 non-radioactive.
- 6th DNA molecule: 1 radioactive + 1 non-radioactive.
- 7th DNA molecule: 1 radioactive + 1 non-radioactive.
- 8th DNA molecule: 1 radioactive + 1 non-radioactive.

**Total radioactive DNA molecules after 3rd duplication**: 4 (2 from each of the original 4)

### Conclusion
After three duplications, there are **4 DNA molecules that contain radioactive thymidine**.

### Final Answer
**4 DNA molecules contain radioactive thymidine after 3 duplications.**