Question

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

Answer 1

`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"`