What proportion of dna molecules will contain any radioactivity after two rounds of replication?

After two rounds of replication half of DNA molecules will contain one strand with radioactive nitrogen. And the other half will contain two strands with radioactive nitrogen.

Explanation:

In semi-conservative replication, two DNA molecules are created, each consisting of one strand of the original DNA and one new complementary strand. In other words, the DNA is formed from one old strand and one new strand. And the existing strands serve as a complementary mould to the new ones.  

Meselson-Stahl's experiment involves growing the bacterium Escherichia coli in a medium containing radioactive nitrogen. Watson and Crick had predicted that DNA replication was semi-conservative, if so the DNA extracted from the bacteria would be somewhere in between the DNA extracted from the "normal" nitrogen medium and the radioactive nitrogen medium.

DNA replication, which occurs only once in each cell generation, requires many "building blocks", enzymes, and a great deal of energy in the form of ATP. The nucleotides, which are the building blocks of DNA, have to be assembled and available in the nucleus along with the energy to bind them together.  Each nucleotide consists of three parts: a nitrogen-containing ring structure called a nitrogen base, a five-carbon sugar, and at least one phosphate group.

Through the action of DNA polymerase during replication, new nucleotides bind to the corresponding nucleotide of the original chain (A to T, C to G).

Since the DNA strands are anti-parallel, and replication proceeds only in the 5' to 3' direction on both strands, one strand will form a continuous copy, while the other will form a series of short fragments known as Okazaki fragments. The chain that is synthesized continuously is known as the forward chain and the chain that is synthesized in fragments is known as the backward chain.

Then, since replication is semi-conservative, the new strand will have nucleotides with "normal" nitrogen while the new strand created from that same DNA molecule will incorporate nucleotides with radioactive nitrogen. So, after two rounds of replication half of DNA molecules will contain one strand with radioactive nitrogen. And the other half will contain two strands with radioactive nitrogen.