**Core Concept**
The process of DNA replication involves the unwinding of double-stranded DNA into two single strands, followed by the synthesis of new complementary strands. In a completely radioactive double-stranded DNA molecule, both strands are initially labeled with radioactive isotopes. During replication, each parent strand serves as a template for the synthesis of a new complementary strand.

**Why the Correct Answer is Right**
When the radioactive double-stranded DNA molecule undergoes the first round of replication, two new double-stranded DNA molecules are formed. One parent strand from the original molecule and one newly synthesized strand will be radioactive, while the other two strands will be non-radioactive (newly synthesized). In the second round of replication, each of the four resulting strands (two radioactive and two non-radioactive) will serve as a template for the synthesis of a new complementary strand. As a result, two new double-stranded DNA molecules will be formed with two radioactive strands each, and two will have two non-radioactive strands each.

**Why Each Wrong Option is Incorrect**
* **Option A:** This option would imply that all four resulting DNA molecules have the same radioactivity status, which contradicts the mechanism of DNA replication.
* **Option B:** This option suggests that all four resulting DNA molecules are non-radioactive, which is not possible since the original DNA molecule was completely radioactive.
* **Option D:** This option implies that only two of the resulting DNA molecules are radioactive, which is not consistent with the replication process.

**Clinical Pearl / High-Yield Fact**
In DNA replication, each new strand is synthesized by adding nucleotides complementary to the template strand, resulting in a 5' to 3' phosphodiester bond.

**Correct Answer: C.**