Radioactive isotopes are often introduced into the body through the bloodstream.
ID: 1304735 • Letter: R
Question
Radioactive isotopes are often introduced into the body through the bloodstream. Their spread through the body can then be monitored by detecting the appearance of radiation in different organs. 131I, a ?? emitter with a half-life of 8.00d, is one such tracer. Suppose a scientist introduces a sample with an activity of 425Bq and watches it spread to the organs
Assuming that the sample all went to the thyroid gland, what will be the decay rate in that gland 24.0d(about 312 weeks) later?
If the decay rate in the thyroid 24.0d later is actually measured to be 17.0Bq , what percent of the tracer went to that gland?
Explanation / Answer
A)
We are asked for the decay rate (which means the same as activity) after 24 days.
The half life is 8 days.
After 8 days the activity is halved: A = 425/2 = 212.5Bq
After a further 8 days the activity is halved again: A = 212.5/2 = 106.25Bq
After a further 8 days the activity is halved again: A = 106.25/2 = 53.125Bq
So after three lots of 8 days (i.e. 24 days in total) the activity is 53.125Bq. Round this to 53Bq.
Of course you don't have to write all that out. More briefly we can say:
24 days = three half lives (because 3x8=24).
The remaining activity is 425/(2x2x2) = 53Bq approx
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B)
The decay rate from the full amount of tracer would be 53.125Bq.
The actual decay rate = 17Bq.
The decay rate is proportional to the amount of tracer.
So the % of tracer in the thyroid = (17/53.125) x 100 = 32%
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