Step 1: Understanding the Concept:
Phosphorus-32 ($^{32}\text{P}$) is a high-energy $\beta$-emitting radioisotope widely used for nucleic acid radiolabeling in molecular biology. Key Formula or Approach:
\[ N(t) = N_0 \left(\frac{1}{2}\right)^{\frac{t}{t_{1/2}}}, \quad t_{1/2}(^{32}\text{P}) \approx 14.29\text{ days} \] Step 2: Detailed Explanation: Phosphorus-32 ($^{32}\text{P}$): - Pure $\beta^-$-emitter ($E_{\max} = 1.71\text{ MeV}$) used to label nucleotides at the $\alpha$- or $\gamma$-phosphate position for Southern blotting, Northern blotting, DNA sequencing, and kinase assays. - Its radioactive half-life ($t_{1/2}$) is 14.28 days ($\approx 14$ days). (Compare with $^{35}\text{S} = 87.4\text{ days}$, $^{14}\text{C} = 5730\text{ years}$, $^{131}\text{I} = 8.02\text{ days}$, $^{45}\text{Ca} = 163\text{ days}$). Step 3: Final Answer:
Thus, the half-life of 32P is 14 days, matching option (C).
