The specific rate constant (\(k\)) for polonium-211 is approximately \(1.332 \, \text{s}^{-1}\), calculated using its half-life (\(t_{1/2}\)) and the relationship \(k = \frac{\ln(2)}{t_{1/2}}\).
The half-life (\(t_{1/2}\)) of a radioactive isotope is related to the specific rate constant (\(k\)) by the equation \(t_{1/2} = \frac{\ln(2)}{k}\). For polonium-211, with a half-life of 0.52 seconds, we can rearrange the equation to solve for \(k\): \(k = \frac{\ln(2)}{t_{1/2}}\). Substituting the given values:
\[ k = \frac{\ln(2)}{0.52 \, \text{s}} \]
\[ k \approx \frac{0.693}{0.52} \, \text{s}^{-1} \]
\[ k \approx 1.332 \, \text{s}^{-1} \]
Therefore, the specific rate constant (\(k\)) for polonium-211 is approximately \(1.332 \, \text{s}^{-1}\).