Im stuck on this study question.
It says.
Iodine-135 has a half life of 8 days. How long would it take for 28kg of iodine-135 to decay to 200g?
The answer s 57.03 days.
Could someone explain how this answer was gotten? The unit is logarithmic funtions so I assume that they are involved, but how?
Hello, Skor!
There is a half-life formula, but we can derive it ourselves.Iodine-135 has a half-life of 8 days.
How long would it take for 28 kg of Iodine-135 to decay to 200 g?
The answer s 57.03 days.
Assume an exponential function:
. . where is the amount of I-135 at time (days).
Let = original amount of I-135.
At the very beginning , we have: .
In 8 days, only half of the I-135 remains. .That is, when
So we have: .
Rewrite in logarithmic form: .
. . Hence:. .
Therefore, the function is: .
We are told that: . and
So we have: .
. .
Therefore: .