Question

A certain nuclide has a half-life period of 30 min. If a sample containing $600$ atoms is allowed to decay for $90$ min, how many atoms will remain?

• A. $200$ atoms
• B. $450$ atoms
• C. $75$ atoms
• D. $150$ atoms

Answer 1

The correct option is C $75$ atoms

$n=\frac{totaltime}{half-lifeperiod}=\frac{90}{30}=3$
$N=N_o\times {\left(\frac{1}{2}\right)}^n$
$=600\times {\left(\frac{1}{2}\right)}^3$
$=\frac{600}{8}$
$=75$ atoms