Final answer:
Morgan concluded the white-eye gene was on the X chromosome because white eyes appeared only in the male F2 offspring, consistent with the characteristics of X-linked inheritance and male hemizygosity.
Step-by-step explanation:
Morgan thought the gene involved in his white-eyed mutant was located exclusively on the X chromosome, with no corresponding allele present on the Y chromosome, because of the distinctive patterns observed in the offspring of his Drosophila crosses.
When crossing red-eyed females with white-eyed males, the F1 generation displayed red eyes, indicating the dominance of the red eye color gene. However, in the F2 generation, the appearance of white-eyed males but not white-eyed females suggested that the white-eye mutation was X-linked.
Males being hemizygous, having only one X chromosome, lack a second allele of the eye-color gene on the Y chromosome, so their genotype can only be XWY (red-eyed) or XY (white-eyed), while females with two X chromosomes can be XWXW (red-eyed), XWX (red-eyed), or XX (white-eyed).