What is the mass of $25.0 \mathrm{mCi}$ of technetium- $99 \mathrm{~m}$ (Tc99m), which has a half-life of $6.00 \mathrm{~h}$ ?

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To find the mass of $25.0 \mathrm{mCi}$ of technetium-99m, we use the formula relating activity (A) to the number of nuclei (N), half-life (T), and decay constant ($\lambda$): $A = \lambda N$. The decay constant $\lambda$ can be found from the half-life using $\lambda = \frac{\ln(2)}{T}$. Given the half-life $T = 6.00$ hours, we convert it to seconds to use SI units: $T = 6.00 \times 3600 \, \text{s}$. The activity $A = 25.0 \, \text{mCi}$ is converted to becquerels (Bq) using $1 \, \text{Ci} = 3.7 \times 10^{10} \, \text{Bq}$, so $A = 25.0 \times 10^{-3} \times 3.7 \times 10^{10} \, \text{Bq}$. With $\lambda$ and $A$, we solve for $N$, and then use $N = \frac{m}{M}$ to find the mass $m$, where $M$ is the molar mass of technetium-99m. Given the atomic mass of technetium ($\approx 98 \, \text{g/mol}$), the calculation yields a mass in the nanogram range, matching the value in choice A.

What Is the Mass Of 25.0mCi25.0 \mathrm{mCi}25.0mCi Of Technetium- 99 m99 \mathrm{~m}99 m (Tc99m), Which Has a Half-Life Of

What Is the Mass Of $25.0 \mathrm{mCi}$ Of Technetium- $99 \mathrm{~m}$ (Tc99m), Which Has a Half-Life Of