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Radioactive isotopes are often introduced into the body through thebloodstream.

ID: 2021018 • Letter: R

Question

Radioactive isotopes are often introduced into the body through thebloodstream. Their spread through the body can then be monitored bydetecting the appearance of radiation in different organs.^{131}I, a eta ^ - emitter with a half-lifeof 8.00 { m d}, is one such tracer. Supposea scientist introduces a sample with an activity of425 { m Bq} and watches it spread tothe organs.

Assuming that the sample all went to the thyroid gland, what willbe the decay rate in that gland 24.0 { m d} (about 3({1}/{2})weeks) later?
If the decay rate in the thyroid 24.0 { m d} later is actually measuredto be 17.0 { m Bq}, what percent of the tracerwent to that gland?

Explanation / Answer

GIven Half life   I - 131   T1/2 = 8 days inital activity of the sample   Ao = 425 Bq decay constant   = 0.693 / T 1/2                                = 0.693 / 8                                 = 0.086625 days -1 Activity of the sample after 24 days is      A = A o e -t          = 425 ( e -(0.086625)(24)           = 53.148 Bq ______________________________________________ If the decay rate of the sample in the gland is 17 Bq percentage of tracer went to the gland i s                    = 425 - 17 / 425                     = 96 %