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

Activity of the sample is $R=1500 Ci=1500(3.7*10^{10})$

$=5.55*10^{13} decays/s$

The expression for the activity of the sample is

$R= \frac{ln2 N_A m}{M T_{1/2}}=\frac{0.693 N_A m}{M T_{1/2}}$

Here $N_A$ Avogadro number.

$m$ is the mass of sample.

$M$ is the molecular mass.

Isolate the above equation for $m$ ,

$m=\frac{RM T_{1/2}}{0.693 N_A}$

$=\frac{(5.55*10^{13})(206.977*10^{-3})(4.77*60)}{0.693 (6.022*10^{23})}$

$=7.99*10^{-9} kg=7.99*10^{-6} g =7.99 \mu g$