8. (20 points) A blood-volume determination was carried out on a patient by inje

Question

8. (20 points) A blood-volume determination was carried out on a patient by injection with 20 mL of blood that had been radioactively labeled with 51 Cr to an activity of 4.10 Ci/mL. After a brief period to allow for mixing in the body, blood was drawn from the patient for analysis. Unfortunately, a mix-up 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 then determined to be 0.00935 Ci/mL 51 Cr has a half-life (t1/2) of 27.7 days. Determine the blood volume of the patient from the above information. (For the first order process of radioactive decay, In(N/No)-kt)

Explanation / Answer

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

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