Question

The radioactive isotope sodium-24 is used as a tracer to measure the rate of flow in an artery or vein. The half-life of sodium-24 is 14.9 hours. Suppose that a hospital buys a 20-g sample of sodium-24.
(a) How much of the sample will remain after 48 hours? (Round your answer to two decimal places.)
??? g

(b) How long will it be until only 1 gram remains? (Round your answer to the nearest whole number.)
??? hr

Answer 1

a) Since the half-life of the isotope is 14.9 hours, 48 hours is 3.2215 half-lives.
The initial amount of the isotope is 20g. Half of it goes away every half-life.
\[A=20(\frac{1}{2})^{48/14.9}=20(0.10721)=2.14 g\]

b) We set up the same equation, except the time is unknown and A = 1.
\[1=20(\frac{1}{2})^t\]Solve for t.