Question

The half-life of a radioisotope is 10 h. Find the total number of disintegrations in the tenth hour measured from a time when the activity was 1 Ci.

Answer 1

Given $t_{\frac{1}{2}}=1602\text{years}$

$Ra=226\text{g/mole}$

$\text{Ci}=35.5\text{g/mole}$

$1{\text{mole Ra Cl}}_2=226+71=297g$

$297g={\text{1 mole of RaCl}}_2=\frac{0.1\times 6.023\times {10}^{2}8}{297}$

$=0.02027\times {10}^{22}$

$\lambda =\frac{0.693}{t_{\frac{1}{2}}}$

$=\frac{0.693}{1602\times 365\times 24\times 3600}$

$=1.371\times {10}^{-11}$

$\text{Activity}=\lambda N$

$=1.371\times {10}^{-11}\times 2.07\times {10}^{20}$

$=2.779\times {10}^9$

$=2.8\times {10}^9\text{disins. / sec}$