A small quantity of solution containing `Na^(24)` radio nuclide of activity 1 microcurie is injected into the blood of a person. A sample of the blood of volume `1 cm^(3)` taken after 5 h shows an activity of 296 disintegration per minute. What will be the total value of the blood in the person? Assum that the radioactive solution mixes uniformly in the blood of the person. (Take, 1 curie `= 3.7xx10^(10)` disintegration per second and `e^(-lamdat)=0.7927,` where lamda=` disintegration constant)

Answer

A, C

Explanation

:' `lambda=`Disintegration constant
`0.693/t_(1//2)=0.693/15h^-1=0.0462h^-1`
Let `R_0=` initial activity = 1 microcurie `=3.7 xx 10^4` disintegrations per second
`r=` Activity in `1 cm^3` of blood at `t=5h`
`=296/60` disintegration per second
`=4.93 disintegration per second, and
`R=` Activity of whole blood at time `t=5h`
Total volume of blood should be
`V=R/r=(R_0e^(-lambdat))/r`
Substituting the values, we have
`V=((3.7xx10^4)/(4.93))e^(-(0.0462)(5))cm^3`
`V=5.95xx10^3cm^3` or
`V=5.95L`