In an experiment concerning radioactive decay, the count rate of radiation 5 cm from a
source X was measured as 140 counts per minute. 12 minutes later, with the detector in the
same position, the count rate was measured as 35 counts per minute.
Background radiation was recorded as 20 counts per minute.
Calculate the half-life of source X. (Give your answer in minutes.)

Answer:

15) 4 minutes

Initial count rate = 140 – 20 (background radiation) = 120
Final count rate = 35 – 20 = 15
We need to figure out the number of half lives.

120 → 60 = 1 half life

60 → 30 = 2 half lives

30 → 15 = 3 half lives

There were three half lives over the period of 12 minutes

Time per half life = 12 ÷ 3 = 4 minutes