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A small quantity of solution containing `Na^24` radio nuclide `(half-life=15 h)` of activity `1.0 microcurie` is injected into the blood of a person. A sample of the blood of volume `1cm^3` taken after `5h` shows an activity of `296` disintegrations per minute. Determine the total volume of the blood in the body of the person. Assume that the radioactive solution mixes uniformly in the blood of person.
(1 curie `=3.7 xx 10^10` disintegrations per second)

Text Solution

Verified by Experts

The activity varies according to the equation, `A(t)= A_(0) e^(-lambdat)`, or, `A(t)= A_(0) ((1)/(2))^((t)/((T)_((1)/(2)))`, In the problem , A(t=5hr)=296 disintegrations /min, `(296)/(60)=A_(0)((1)/(2))^((5)/(15))`or, `A_(0)=(296)/(60)xx2^((1)/(3))=6.22` disintegration /sec,= the initial activity of `1_cc`. of blood.If the volume of blood is `V_cc`,`6.22V=3.7xx10^(10)xx10^(-6) implies,V=5.9l`.
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