Q 12-13-005NEETNEET 2021Top questionMedium
The half-life of a radioactive nuclide is $100$ hours. The fraction of original activity that will remain after $150$ hours would be :
Answer: (C) $\dfrac{1}{2\sqrt{2}}$
Concept. $\dfrac{A}{A_0} = \left(\dfrac12\right)^{t/T_{1/2}}$, valid for any (also non-integer) number of half-lives.
Step 1. Number of half-lives. $\dfrac{150}{100} = \dfrac32$.
Step 2. Fraction.
$$\left(\frac12\right)^{3/2} = \frac{1}{2\sqrt2}$$
Answer. $\dfrac{1}{2\sqrt2}$ (Option C).
Solution by Sreeraj P, M.Sc Physics