Question

A radioactive sample of thallium-207 has a half-life of 4.77 minutes has an activity of 1500 Ci.
What is the mass of the sample of thallium? (to 2 s.f and in µg)

Answer 1

From the formula for the activity of a substance

$C=\frac{0.693 \cdot N_A \cdot m}{M \cdot T_{1/2}}$

Where

$N_A=6.022 \cdot 10^{26}$ - Avogadro number

$M$ - atomic mass of the radioactive element

$T_{1/2}=4.77 \cdot 60=286.2 s$ - half-life of a radioactive element

$m$ -mass of a radioactive element

Note

$m=\frac{C \cdot M \cdot T_{1/2}}{0.693 \cdot N_A}$

Given that

$1Ci=3.7 \cdot 10^{10}{decays}/s$

$m=\frac{1500 \cdot 206.977 \cdot( 4.77\cdot 60 )\cdot 3.7 \cdot 10^{10} \cdot 10^{6}}{0.693 \cdot 6.022 \cdot 10^{26}}=7.878 \cdot 10^{-3}\mu g$