Question

A radioactive isotope of potassium (K) has a half-life of 20 minutes. If a 40.0 gram sample of this isotope is allowed to decay for 80 minutes, how many grams of the radioactive isotope will remain?

A) 2.5 grams
B) 5.0 grams
C) 10.0 grams
D) 40.0 grams

Answer 1

A) 2.5 grams

Step-by-step explanation:

Because it goes through 80 minutes, this is 4 half-lives, 80/20=4. During each half life, the amount is reduced by a factor of 1/2. So, it goes from 40g to 20g, 20g to 10g, 10g to 5g and finally, 5g to 2.5g.

Answer 2

The answer is A) 2.5 grams

The formula for half-life is:

Remaining Amount = Initial Amount * (1/2)^(time of decay/half-life)

For this problem you'd set up the formula like this:

x = 40 * (1/2)^(80/20) ... which simplifies to
x = 40 * (1/2)^4 ... which simplifies to
x = 40 * .0625

which makes x 2.5 grams