If the half-life of a radioactive element is T, then the number of nuclei remaining after time t will decrease from No to N:
N = N0 * 2 ^ (- t / T);
In our case, the decay time is equal to 4 half-lives:
t = 4T;
N = N0 * 2 ^ (- 4T / T) = N0 * 2 ^ (- 4) = N0 / 16.
The number of decayed nuclei:
N0 – N = N0 – N0 / 16 = (15/16) N0.
Answer: 15/16 nuclei of a radioactive element will decay in 4 half-lives.
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