Radioactive isotopes are often introduced into the body through thebloodstream.

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 %

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