SOLUTION: please help me to solve the problem-In how many years will a given quantity of Iodine 131 lose 80% of its radioactivity? (Note: The half life of Iodine-131 is 8 days)

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Question 1057866: please help me to solve the problem-In how many years will a given quantity of Iodine 131 lose 80% of its radioactivity? (Note: The half life of Iodine-131 is 8 days)

Answer by math_helper(2461) About Me  (Show Source):
You can put this solution on YOUR website!
Half life = 8 days
+t_halflife+=+ln%282%29%2Flambda+
+++8+=+0.69315%2Flambda+
+++lambda+=+0.69315%2F8+=+0.08664+
Now use the decay formula:
+N+=+%28N_o%29e%5E%28-lambda%2At%29+
Given N=20% of N_o (80% loss of radioactivity ==> 20% remaining)
+0.20+=+e%5E%28-0.08664%2At%29+
+ln%280.20%29+=+-0.08664%2At+
+-1.6094+=+-0.08664%2At+
+18.576+=+t+
—
Ans: In 18.576 days, the Iodine-131 will have lost 80% of its radioactivity.
(18.576 days is equivalent to 0.051 years)