Medical Imaging Systems · Nuclear Imaging · 2 marks · Numerical answer
The half-lives of ¹¹³ᵐIn and ⁹⁹ᵐTc are 1.7 and 6.0 hours. Their initial sample activities are 100 and 20 GBq respectively. After how many hours are their activities equal, rounded to one decimal place?
Radioactive activities decay as A=A0×2^(−t/T½). Equality gives 100×2^(−t/1.7)=20×2^(−t/6). Taking natural logs gives t=ln5/[ln2(1/1.7−1/6)]≈5.51 hours, rounded to 5.5. This is the shared-activity time, not a half-life of a mixture.
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