Step by step
The question
Question: A substance has a half-life of 6 years.
How much of 120 g is left after 24 years?
1 Count the half-lives
Every 6 years, half is left.
Half means times 1/2.
every 6 years: × 12
How many half-lives in 24 years?
24 divided by 6: 4.
half-lives = 246 = 4
Careful!
4 half-lives is not divided by 4.
It is halved 4 times, one after another.
Careful: not 120 ÷ 4 = 30 g ✗
2 Halve it that many times
A = the start times (1/2) to the power 4.
A = 120 × (12)4
(1/2) to the power 4 is 1/16.
(12)4 = 116
120 times 1/16 is 120/16.
A = 12016
120 divided by 16 is 7.5 g.
A = 7.5 g
3 Check
Let's check, half-life by half-life.
Every 6 years, we halve it.
After 24 years we get 7.5 g again.
It works!
after 24 years: 7.5 g
Let's look back.
First: count the half-lives.
Then: halve it that many times.
Last: check.
Answer
A = 7.5 g