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Q. The half-life of a radioactive isotope is three hours. If the initial mass of the isotope were $256 \,g$, the mass of it in grams remaining undecayed after $18$ hours would be:

NTA AbhyasNTA Abhyas 2022

Solution:

$t_{1 / 2}=\text{3 hours, }n=\text{T}/t_{1 / 2}=18/3=6$
$\text{N} = \left(\text{N}\right)_{0} \left(\frac{1}{2}\right)^{6}$
$= 2 5 6 \times \frac{1}{8} \times \frac{1}{8} = \text{4} \text{g} \cdot $