As part of her nuclear stress test, Simone starts to walk on the treadmill. When

Question

As part of her nuclear stress test, Simone starts to walk on the treadmill. When she reaches the maximum level, Paul injects a radioactive dye with 201Tl with an activity of 68 MBq . The radiation emitted from areas of her heart is detected by a scanner and produces images of her heart muscle. After Simone rests for 3 h, Paul injects more dye with 201Tl and she is placed under the scanner again. A second set of images of her heart muscle at rest is taken. When Simone's doctor reviews her scans, he assures her that she had normal blood flow to her heart muscle, both at rest and under stress.

Part A If the half-life of 201Tl is 3.0 days, what is its activity, in megabecquerels after 3.0 days? Express the activity to two significant figures and include the appropriate units.

Part B What is its activity in megabecquerels after 12.0 days? Express the activity to two significant figures and include the appropriate units.

Explanation / Answer

A)

we know that

for radioactive decay

A = Ao x e^(-kt)

ln A = lnAo - (kt)

now

we know that

rate constant (k) = ln2 / half life

so

rate constant (k) = ln2 / 3

rate constant = 0.23104906

now

given

time (t) = 3 days

initial activity (Ao) = 68

so

ln A = ln 68 - ( 0.23104906 x 3)

A = 34

so

the activity after 3 days is 34 MBq

B)

time (t) = 12 days

initial activity (Ao) = 68

so

ln A = ln 68 - ( 0.23104906 x 12)

A = 4.25

so

the activity after 12 days is 4.25 MBq

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