After 4 hours, \( \frac{1}{16} \) of the initial amount of a certain radioactive isotope remains undecayed. What is the half life of the isotope?
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → 60 min
In each half-life the undecayed amount falls to half. After \( n \) half-lives the fraction left is
\( \displaystyle \frac{N}{N_0} = \left(\frac{1}{2}\right)^{n} \)
\( \displaystyle \frac{1}{16} = \left(\frac{1}{2}\right)^{4} \;\Rightarrow\; n = 4 \)
So 4 half-lives pass in 4 hours.
\( \displaystyle T_{1/2} = \frac{4\,\mathrm{h}}{4} = 1\,\mathrm{h} = 60\,\mathrm{min} \)