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Hi there.
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So for this problem, we are told that 10 grams of plutonium 239, isotope were released in a nuclear accident.
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Now, if the half -life of plutonium 239 is given, and that is equal to 24 ,100 years.
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So the question is, how long will it take for the 10 grams to break? down to 1 gram.
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So we need to pass from the 10 initial grams to 1 grams.
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So with that set, we start by the function of the amount that we will have a plutonian.
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That will be equal to a constant c times the exponential of a constant of proportionality k times the time.
01:19
Now in here we substitute the conditions for the half -life.
01:23
We know that for half life, we will have half of the amount, so that will be five.
01:30
And this is equal to 10 times the exponential of 24 ,000 and 100 times the constant k.
01:43
So we can pass to this and the 10 to the left side.
01:48
So we obtain 1 divided by 2 is equal to the exponential of 24 ,000 and 100 times.
01:54
The constant k.
01:57
So since we want to obtain the constant k, we can apply the nepearian logarithm to both sides.
02:04
So we obtain that this constant is just simply the neferian logarithm of 1 divided by 2 and this divided by 24 ,100...