SOLUTION: An unknown radioactive element decays into non-radioactive substances. In 560 days the radioactivity of a sample decreases by 51 percent.
(a) What is the half-life of the eleme
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Question 1136372: An unknown radioactive element decays into non-radioactive substances. In 560 days the radioactivity of a sample decreases by 51 percent.
(a) What is the half-life of the element?
half-life:
(days)
(b) How long will it take for a sample of 100 mg to decay to 47 mg?
time needed:
Found 2 solutions by josgarithmetic, greenestamps:
Answer by josgarithmetic(39617) (Show Source): You can put this solution on YOUR website!
------first step is to find the value of k.
-
MODEL:
Note that the half life will be very close to 560 days.
More like 546 days.
Answer by greenestamps(13200) (Show Source): You can put this solution on YOUR website!
The fraction of the material remaining after n half-lives is
(a) Determine the half-life
In this problem, the amount of material decreased by 51% in 560 days; that means after 560 days 49% remains. Use the basic formula to determine how many half-lives that is.
n = 1.0291463 (to several decimal places, using a graphing calculator)
So the half-life of the material is
(b) Determine how long it will take a 100mg sample to decay to 47mg
Use the basic formula to determine the number of half-lives it takes for the material to decay to where 47% remains, then multiply the half-life by that number.
It takes about 593 days for a 100mg sample to decay to 47mg.
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