Question

Upon irradiating californium with neutrons, a scientist discovered a new nuclide having mass number of $250$ and a half-life of $0.50hr$. Three hours after the irradiation, the observed radioactivity due to the nuclide was $10dis/min$. How many atoms of the nuclide were prepared initially?

Answer 1

$t1/2=0.5$ hr

$t=3$ hr

$R=10$ dis/min

$Ro=?$

$3=\frac{2.303\times 0.5}{0.693}\times log\left(\frac{Ro}{10}\right)$

$Ro=638.9$

i.e. $Ro=639$ dis/min

No. of atoms initially $=639$.