Two radioactive sources X and Y have half-lives of 4.8 hours and 8.0 hours respectively. Both decay directly to form only stable isotopes. The activity of a sample of the source X was measured by a detector as 320 counts per minute, and simultaneously the radioactivity of a sample of the source Y was measured as 480 counts per minute. Immediately after the measurements, the two samples were combined. What was the count rate when the activity of the combination of X and Y was measured 24 hours later?[Assume that all readings in this question have been corrected for background radiation.]

Answer:

15) D

Half-life of X = 4.8 hours
Number of half lives of X in 24 hours = 24 ÷ 4.8 = 5
Count rate of X after 5 half lives = 320 ÷ 2⁵ = 10

Half-life of Y = 8 hours
Number of half lives of X in 24 hours = 24 ÷ 8 = 3
Count rate of Y after 3 half lives = 480 ÷ 2³ = 60

Total count rate = 10 + 60 = 70