Answer
After 18 hours, 10.0 mg of technetium-99m will remain.
Work Step by Step
1. Use the half life value for $^{99m}_{43}Tc$ as a conversion factor to calculate the amount of half-lives after 18 hours.
number of half lives = $18 h \times\frac{1 half-life}{6.0 min} = 3.0$ half-lives.
2. After a half-life, one-half of the technetium-99m decays. Therefore, the remaining mass is equal to $\frac{1}{2}$ of the initial mass.
Initial $^{99m}_{43}Tc$ mass: 80.0 mg
After one half-life:
$80.0$ $mg$ $\times \frac{1}{2} = 40.0$ $mg$
3. The same will occur on the following half-lives, so, repeat the process:
After the second half-life:
$40.0$ $mg$ $\times \frac{1}{2} = 20.0$ $mg$
After the third half-life:
$20.0$ $mg$ $\times \frac{1}{2} = 10.0$ $mg$
