I need help with this question it relates to blood volume in a medical setting?

You inject a 160 Ib male patient with 1.0 mL of a saline solution containing a radioactive form of sodium. It has an activity of 5.0 x 10^4 dpm. After allowing sufficient time for the solution to mix, you remove a 1.0 ml sample of blood and measure its radioactivity. You discover it to have an activity of 11 dpm. What is the patient's blood volume

1 Answer
A08
May 24, 2016

#approx4.544" L"#

Explanation:

Let the blood volume of patient be #=n " mL"#
After injecting saline solution new volume of blood #=n+1" mL"#
DPM of #1 " mL"# injected sample#=5.0 xx 10^4#

Assuming there is no change in activity of sample during the time when two mix together.
DPM of #1 " mL"# extracted sample#=(5.0xx10^4)/(n+1)# .....(1)
Measured DPM of #1 " mL"# extracted sample#=11# ......(2)
Equating (1) and (2)

#(5.0xx10^4)/(n+1)=11#
#(n+1)xx11=5.0xx10^4#, solving for #n#
#11n=5.0xx10^4-11#
#n=4544.bar45" mL"#
#napprox4544" mL"#

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