SOLUTION: The half-life for thorium-227 is 18.72 days. The amount A (in grams) of thorium-227 after t days for a 10-gram sample is given by A(t)=10⋅0.5^t/18.72 How long will it take bef

Question 1156050: The half-life for thorium-227 is 18.72 days. The amount A (in grams) of thorium-227 after t days for a 10-gram sample is given by A(t)=10⋅0.5^t/18.72
How long will it take before 3 grams of thorium-227 is left in the sample? Round your answer to the hundredths place.
....days
Thank you
Answer by greenestamps(13200) (Show Source): You can put this solution on YOUR website!

= 32.515995..., or 32.52 to the nearest hundredth.

ANSWER: 32.52 days

-------------------------------------------

Added comment....

I find that using the given formula to solve the problem adds an unnecessary level of difficulty to the problem. I would much rather simply solve for the number of half-lives and multiply that answer by the given length of the half-life.

t = 18.72*1.7369656 = 32.515995....

This method of solving the problem has a huge advantage if you are solving a large number of similar problems involving half-lives.

If the problems are with all different half-lives, then solving the problem by the first method shown involves a different first calculation for every problem; with the second method, the first calculation is always the same, and then you just need to multiply the result of that calculation by the half-life.

Someone who works this kind of problem often would undoubtedly work the problem this way.

For example, suppose we have an initial amount 23 and a final amount 5, with a half-life of 385 years. The calculations would be

(1) find the number of half-lives:
= 2.201634....
(2) multiply by the half-life:
= 847.63 years

RELATED QUESTIONS
hi can someone please help? thanks A 300 g sample of thorium-234 has a half-life of 24... (answered by jim_thompson5910)

A 300g sample of thorium-234 has a half-life of 24 days. The mass of thorium, in grams,... (answered by ankor@dixie-net.com)

The mass m(t) remaining after t days from a 25-g sample of thorium-234 is given by... (answered by stanbon)

Can some please help me? The half life of Thorium-232 is 14 billion years. Make a table... (answered by scott8148)

The half-life of tritium is 12.4 years. How long will it take for 15% of a sample of... (answered by stanbon)

Osmium has a radioactive isotope that has a half life of 15.4 days. If one gram of the... (answered by scott8148)

An isotope of thorium, 227Th, has a half-life of 18.4 days. How long will it take for 85% (answered by jsmallt9)

PLEASE HELP!! The radioactive isotope thorium 234 has a half-life of approximately 578... (answered by stanbon,Theo)

The half life of a particular radioactive isotape of thorium is 8 minute. Find an... (answered by stanbon)