Final answer:
Breaks in double-stranded DNA molecules are most commonly a result of exposure to ionizing radiation such as X-rays and gamma rays, which break the DNA backbone and modify bases.
Step-by-step explanation:
Breaks in double-stranded DNA molecules are most likely to result from exposure to ionizing radiation. Ionizing radiation, such as X-rays and gamma rays, can cause single- and double-stranded breaks in the DNA backbone. This occurs through the formation of hydroxyl radicals upon exposure to ionizing radiation. Breakage of the phosphodiester backbone of DNA by ionizing radiation can also lead to chemical modifications of bases, affecting their pairing rules.