Final answer:
The false statement is that primates, dogs, mice, and chickens all have about the same number of genes. While most mammals have a similar number of genes, chickens typically have fewer, and the similarity in gene number across these species is not as uniform as option 2 wrongly suggests.
Step-by-step explanation:
The statement which is false is: A comparison of genomes shows that primates, dogs, mice, and chickens all have about the same number of genes. This is not accurate, as genome comparisons reveal that while primates (including humans), dogs, and mice have a similar number of genes, chickens tend to have fewer.
The human genome has roughly 20,000-25,000 genes, which is comparable to other mammals. Chickens, being from a different class of vertebrates (birds), have some differences in their genome and typically fewer genes than most mammals.
It is true that the human genome is closer to the orangutan genome than to the mouse genome because orangutans are primates like humans, and thus, we share a more recent common ancestor with them. It is also correct that genes coding for ribosomal RNA share significant similarity across all eukaryotes due to their fundamental role in cellular function and have evolved less rapidly, making them more conserved.
However, these genes can still be recognizable but less similar in archaea, which are a different domain of life altogether.The correct option among those provided is therefore 2, as this statement is false in the context of gene number similarity across these species.