Thallium-201, a radioactive isotope used to image the heart, has a half life of 3.05 days. how long would it take for a sample of thallium-201 to decay to 18% of its original activity?

= 7.55 days

Half life is the time taken by a radioactive isotope to decay by half its original amount.

To calculate the new mass or amount;

New mass = Original mass × (1/2)^n ; where n is the number of half lives.

New mass = 18%, while the original mass = 100 %, half life = 3.05 days

18 = 100 × (1/2)^n

(1/2)^n = 0.18

introducing logarithms;

n log 0.5 = log 0.18

n = log 0.18/ log 0.5

  = 2.474

But 1 half life is 3.05 days

Hence; time taken will be;

= 3.05 × 2.474

= 7.55 days

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