Question

A chemist prepares $1.00g$ of pure ${}_6^{11}C$. This isotope has half life of $21$ minutes, decaying by the equation:
${}_6^{11}C{\to }_5^{11}B{+}_1^{0}e$
(a) What is the rate of disintegration per second (dps) at start?
(b) What are the activity and specific activity of ${}_6^{11}C$ at start?
(c) How much of this isotope ${}_6^{11}C$ is left after $24$ hours of its preparation?

Answer 1

(a) Applying, $-\frac{dN}{dt}=\lambda N_0$
$=\frac{0.693}{21\times 60}\times \frac{1\times 6.02\times {10}^{23}}{11}$
$=3\times {10}^{19}dps$
(b) Activity $=\frac{3\times {10}^{19}}{3.7\times {10}^{10}}$ $(1curie=3.7\times {10}^{10}dps)$
$=8.108\times {10}^{8}curie$
Specific activity $=3\times {10}^{19}\times {10}^3=3\times {10}^{22}dis/kgs$
$=8.108\times {10}^{11}curie$
(c) Applying, $N=N_0{\left(\frac{1}{2}\right)}^n$ $[n=\frac{t}{t_{1/2}}=\frac{24\times 60}{21}=68.57]$
$N=1\times {\left(\frac{1}{2}\right)}^{68.57}=2.29\times {10}^{-21}g$