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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)

A

5 94 litre

B

2 litre

C

317 litre

D

1 litre

Text Solution

Verified by Experts

The correct Answer is:
A
`R_(0)= 10^(-6)` Curie `= 3.7 xx 10^(10) xx 10^(-6)` dps
r= Activity in `1cm^(3)` of blood at t= 5 hr
`= (296)/(60)` dps= 4.93 dps
Total volume `V= (R)/(r)= (R_(0)e^(-lamda t))/(r)`
`rArr (3.7 xx 10^(4) xx 0.7927)/(4.93) = 5.94 xx 10^(3) cm^(3)= 5.94` litre
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