A small quantity of solution containing Na24 radio nuclide (half life = 15 hour) of activity 1.0 microcurie is injected into the blood of a person. A sample of the blood of volume 1 cm3 taken. After 5 hour shown an activity of 296 disintegrations per minute. Determine the total volume  of the blood I the body of the person. Assume that radioactive solution mixes uniformly in the blood of the person. (1 curie = 3.7 x 1010 disintegrations per second)

Kevin Nash
9 years ago
Hello Student,
t1/2 = 15 hours
Activity initially A0 = 10-6 Curie (in small quantity of solution of 24Na) = 3.7 x 104 dps
Observation of blood of volume 1 cm3
After 5 hours, A = 296 dpm
The initial activity can be found by the formula
t = 2.303 / λ log10 A0 / A ⇒ 5 = 2.303 / 0.693 / 15 x log10 A0 / 296
⇒ log10 A0 / 296 = 5 x 0.693 / 2.303 x 15 = 0.3010 / 3 = 0.10033
⇒ A­0 / 296 = 1.26 ⇒ A0 = 373 dpm = 373 / 60 dps
This is the activity level in 1 cm3. Comparing it with the initial activity level of 3.7 x 104 dps we find the volume of blood.
V = 3.7 x 104 / 373 / 60 = 5951. 7 cm3 = 5.951 litre
Thanks
Kevin Nash