91Ó°ÊÓ

A radioisotope's half life is the amount of time it takes for one-half of a sample to decay.

Potassium-42 has a half-life of 24 hours. $12\mathrm{h}$.

The sample's activity is $2.0\mathrm{μ}\mathrm{Ci}$after $36\mathrm{h}$

Calculate a sample's starting activity in microcurie.

Calculate half-life conversion factors.

1 half-life $=12\mathrm{h}$

Calculate the number of half-lives in the given amount of time.

After three half-lives, the amount of potassium-42 present is$2.0\mathrm{μ}\mathrm{Ci}$.

Substitute the value in the following scheme according to the definition of half-life period.

$16.0\mathrm{μ}\mathrm{CiK}-42\stackrel{1\text{lulflife}}{âŸ\P }8.0\mathrm{μ}\mathrm{CiK}-42\stackrel{2\text{hall-lives}}{âŸ\P }4.0\mathrm{μ}\mathrm{CiK}-42\stackrel{3\text{bafl-ive}}{âŸ\P }2.0\mathrm{μ}\mathrm{CiK}-42$

As a result, the potassium-42 sample's initial activity is$16.0\mathrm{μ}\mathrm{Ci}$

Calculate the amount of sample that was initially present:

The amount of potassium-42 after three half-lives is present $2.0\mathrm{μ}\mathrm{Ci}$.

Substitute the value in the following scheme according to the definition of half-life period.

$16.0\mathrm{μ}\mathrm{CiK}-42\stackrel{\text{I hufflife}}{âŸ\P }8.0\mathrm{μ}\mathrm{CiK}-42\stackrel{2\text{hasllives}}{âŸ\P }4.0\mathrm{μ}\mathrm{CiK}-42\stackrel{3\text{kalflive}}{âŸ\P }2.0\mathrm{μ}\mathrm{CiK}-42$

As a result, the potassium-42 sample's initial activity is$16.0\mathrm{μ}\mathrm{Ci}$