half life math help please!?

Question

strontium-90 has a half life od 25 years. how much time has elapsed if the following fraction remains in a sample?
1) 1/4
2) 1/32

Answer 1

"Half-life" means that each 50% loss takes 25 years to occur without regard for the amount present (given a reasonably large amount).
So 1/4 is two half lives, which take 50 years.
In a like manner, 1/32 is FIVE half-lives, or 125 years.

Answer 2

Normally you would need the equation of t_1/2=ln(2)/lambda.

In this case you can use simple logic. One half life of St is 25 years in which case 1/2 of the sample remains. In another half life or 50 years, 1/2 of the remaining sample which is 1/2 of the original sample remains, or 1/4 of the original sample, which is your first answer.

You could use that method to find 1/32 because it is a multiple of 2, but that might take a lot of time. Try this instead:

Take the 4 out of 1/4. 4 is 2^2. 32 is 2^5. You can find out the half life by multiplying the half life duration by the power of the fraction (i.e. the 5 in 2^5).

25 years * 2 = 50 years (1/4 remaining)
25 years * 5 = 125 years (1/32 remaining)

Answer 3

rather than using pure mathematics to solve this you can work it out logically,

after 25 years 1/2 will remain. another 25 years after than, 1/2 of 1/2 will remain, or 1/4.

so after 50 years, 1/4 remains.

but another 25 years later (after 75 years) 1/2 of a 1/4 will remain = 1/8. 25 years later (100) 1/16, and finally 25 years after that (125 years) 1/32

Answer 4

amount of halflife= 1, 2, 3, 4, 5, ...
amount left= 1/2, 1/4, 1/8, 1/16, 1/32, ...

1. two half-lives have gone by, so 50 years

2. five haf-lives gone so 125 years

Answer 5

50 years

125 years