After three half-lives, what fraction remains?

A sample initially contains a large number N₀ of one radioactive parent isotope with half-life 4 hours. Consider the sample 12 hours later.

What fraction of the parent nuclei remains undecayed on average?

Organize the givens & assumptions

Half-life: 4 h
Elapsed time: 12 h
Initial parent count: N₀

A single parent isotope with constant decay probability; no new parent nuclei are added. Treat the population as large enough for the exponential law.

A $\tfrac18$
B $\tfrac14$
C $\tfrac13$
D $\tfrac78$

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