Discussion
Nucleus of a radioactive material can undergo beta decay with half life of 4 minutes. Suppose beta decay starts with 4096 nuclei at \(t = 0\), the number of nuclei left after 20 minutes would be
Answer: B
After 20 minutes, 128 nuclei are left.
20 minutes is \(\frac{20}{4} = 5\) half-lives, and each halves the number of undecayed nuclei:
\[ \begin{aligned} N &= 4096 \times \left(\tfrac{1}{2}\right)^{5} \\ &= \frac{4096}{32} = 128 \end{aligned} \]
The other options stop too early: 1024 is after 2 half-lives (8 minutes), 512 after 3 (12 minutes) and 256 after 4 (16 minutes).
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