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What is the half-life of a radioactive isotope if a 500.0 g sample decays to 62.5 g in 24.3 hours?

A. None of these answers
B. 29.3 hours
C. 8.1 hours
D. 13.8 hours
E. 38.1 hours

Answer :

Final answer:

To determine the half-life of a radioactive isotope, you can use the formula half-life = (t2 - t1) / log2(N2 / N1), where t2 is the time passed, t1 is the initial time, N2 is the remaining amount, and N1 is the initial amount.


Explanation:

The half-life of a radioactive isotope can be determined using the formula:



half-life = (t₂ − t₁) / log2(N₂ / N₁)



Where t₂ is the time passed, t₁ is the initial time, N₂ is the remaining amount, and N₁ is the initial amount. Plugging in the given values:



half-life = (24.3 hours − 0 hours) / log2(62.5g / 500.0g)



Calculating this equation will give us the half-life of the radioactive isotope.


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