Question

Bandages can be sterilized by exposure to gamma radiation from cobalt-60, which has a half-life of 5.27 y. How much of a 10.0-mg sample of cobalt-60 is left after one half-life? Two half-lives? Three half-lives?

Answer 1

Step 1

The initial amount of Co-60 = 10.0 g

We need to find the amount of Co-60 left after 1 half-life, 2 and 3 half-lives.

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Step 2

The amount of Co-60 after 1 half-life (n = 1) is:

$\begin{gathered} Amount\text{ remaining = initial amount x \lparen}\frac{1}{2})^n \\ Amount\text{ remaining = \lparen10.0 mg\rparen x\lparen}\frac{1}{2})^1 \\ Amount\text{ remaining = 5.0 mg} \end{gathered}$

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Step 3

For 2 half-lives, n = 2 and initial amount = 10.0 mg, the result is: 2.5 mg

For 3 half-lives, n = 3 and initial amount = 10.0 mg, the result is: 1.25 mg

(The same procedure as step 2)

Answer:

How much of a 10.0-mg sample of cobalt-60 is left after one half-life? 5.0 mg

Two half-lives? 2.5 mg

Three half-lives? 1.25 mg