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Question
A human body excretes (removes by waste discharge, sweating, etc.) certain materials by a law similar to radioactivity. If technetium is injected in some form in a human body, the body excretes half the amount in 24 hours. A patient is given an injection containing 99Tc. This isotope is radioactive with a half-life of 6 hours. The activity from the body just after the injection is 6 μCi. How much time will elapse before the activity falls to 3 μCi?
Solution
Given :
Time taken by the body to excrete half the amount, t1 = 24 hours
Half-life of radioactive isotope, t2 = 6 hours
Initial activity, A0 = 6 μCi
Let after time t, activity of the sample be A.
Half-life period (`T_"1/2"`) is given by
`T_"1/2" = (t_1t_2)/(t_1 + t_2) = (24 xx 6)/(24 + 6)`
= `(24 xx 6)/30` = 4.8 h
Activity (A) at time t is given by
`therefore A = A_0/2^(t/T_"1/2"`
⇒ `3"μCi" = (6"μCi")/2^(t/4.8)`
⇒ `(6"μCi")/2^(t/4.8) = 3`
⇒ t = 4.8 h
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