The half-life of a radioactive substance is the time it takes for half of the substance to decay. The remaining fraction of the original substance after a certain number of half-lives can be calculated using the formula:
N=N0(‌)‌Where:
N is the remaining quantity of the substance,
N0 is the initial quantity of the substance,
t is the elapsed time,
T1∕2 is the half-life of the substance.
Given that the half-life
T1∕2 is 1600 years, and we want to find the amount of substance left after 6400 years, we can use the above formula:
‌=‌=4‌ half-lives ‌Therefore,
‌N=N0(‌)4‌N=N0(‌)‌N=N0(‌)The fraction of the original sample remaining undecayed after 6400 years is
‌.
Thus, the correct answer is:
Option A
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