Question

Cobalt-63 has a half-life of 5.3 years. If a pellet that has been in storage for 15.9 years contains 40.0g of Cobalt-63, how much of this radioisotope was present when the pellet was put into storage? Show work.

Answer 1

320 g

Step-by-step explanation:

The half-life of Co-63 (5.3 yr) is the time it takes for half of it to decay.

After one half-life, half (50 %) of the original amount will remain.

After a second half-life, half of that amount (25 %) will remain, and so on.

We can construct a table as follows:

No. of Fraction Mass

half-lives t/yr Remaining Remaining/g

0 0 1

1 5.3 ½

2 10.6 ¼

3 15.9 ⅛ 40.0

4 21.2 ¹/₁₆

We see that 40.0 g remain after three half-lives.

This is one-eighth of the original mass.

The mass of the original sample was 8 × 40 g = 320 g