A bloodvolume determination was carried out on a patient by

A blood-volume determination was carried out on a patient by injection with 20.0 mL of blood that had been radioactively labeled with Cr-51 to an activity of 4.10 microCi/mL. After a brief period to allow for mixing in the body, blood was drawn from the patient for analysis. Unfortunately, a mixup in the laboratory prevented an immediate analysis, and it was not until 17.0 days later that a measurement on the blood was made. the radiation level was determined to be .00935 microCi/mL. If 51Cr has t1/2=27.7 days, what is the volume of blood in the patient?

Solution

let C= total amount of Cr initially injected

now

activity=k*C/0.020

C=4.10*10^(-6)*0.20/k

now new amount of Cnew=Ce^(-k*t)

k=0.693/T(0.5)=0.0250day^(-1)

Cnew=(blood)*9.35*10^(-9)/k

putting value of Cnew

and substituting theses values

we will get

blood volume=blood=

=5.733litres