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If a radioactive element has a half-life of 4 hours, then x grams of the element dwindles to x/2 grams after 4 hours. If a nuclear reactor has 800 grams of that radioactive element, find the amount of
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May 16, 2024
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If a radioactive element has a half-life of 4 hours, then x grams of the element dwindles to x/2 grams after 4 hours. If a nuclear reactor has 800 grams of that radioactive element, find the amount of radioactive material after 16 hours.
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Answer:
50 grams
Explanation:
The half life = 4 hours; original mass = x grams
That means...
in 4 hours the radioactive element will be reduced to x/2
in 8 hours it will be reduced to 1/2
·
x/2 = x/4
in 12 hours --> 1/2
·
x/4 = x/8
in 16 hours -> 1/2
·
x/8 = x/16
We can determine a general equation for this:
Mass remaining after n hours = x · (1/2)ⁿ
where n = number of half-life periods = time/half life period
Determine how many half-life period there are in 16 hours
= 16/4 = 4. This will be our n
The original mass of the element is 800 grams
Therefore in 4 half-life periods it will reduce to 800 · (1/2)⁴
= 800 · (1/16)
=
50 grams
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Dalloliogm
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May 22, 2024
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Dalloliogm
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