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The half-life of a radioactive substance is 63 years. substance, what fraction will remain in 113 years?



User Cardin
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Final answer:

To find the fraction of a radioactive substance that remains after 113 years, given its half-life is 63 years, we calculate that approximately 1.79 half-lives have passed. The remaining fraction is calculated as (1/2)^1.79, which is approximately 0.292 or 29.2%.

Step-by-step explanation:

The half-life of a radioactive substance is the time it takes for half of the substance to decay. In this question, we need to calculate what fraction of a radioactive substance with a half-life of 63 years will remain after 113 years.

We can use the formula for radioactive decay to find the number of half-lives that have passed. The formula is:

n = t / T1/2

where n is the number of half-lives, t is the total time elapsed, and T1/2 is the half-life of the substance. Using this, we find:

n = 113 years / 63 years = 1.79 half-lives (approximately)

The fraction of the substance remaining after n half-lives is given by:

(1/2)n = (1/2)1.79

Calculating the exponent we get approximately 0.292, which means around 29.2% of the original substance would remain after 113 years.

User Bryan Rowe
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