Question

The half-life of ${}^{226}\text{Ra}$ is 1602 yr. The activity and specific activity of 0.1 g of $RaC{l}_2$ in which all the radium is in the form of ${}^{226}\text{Ra}$ is. The atomic mass of $RaC{l}_2$ is $297gmo{l}^{-1}$.

• A. $[7.5\times {10}^{13}dps;7.5\times {10}^{12}dps]$
• B. $[7.5\times {10}^{12}dps;7.5\times {10}^{13}dps]$
• C. $[2.8\times {10}^{9}dps;2.8\times {10}^{10}dps]$
• D. none of the above

Answer 1

Answer: (C)

$[2.8\times {10}^{9}dps;2.8\times {10}^{10}dps]$

$\lambda =\frac{0.693}{t_{1/2}}=\frac{0.693}{1602\times 365\times 24\times 3600}$
Also activity $\frac{-dN}{dt}=\lambda N=\frac{0.693}{1602\times 365\times 24\times 3600}\times \frac{0.1}{297}\times 6.023\times {10}^{23}=2.78\times {10}^{9}dps$
The specific activity is
$\frac{1}{0.1}\times 2.78\times {10}^{9}dps=2.78\times {10}^{10}dps$