Question

A radioactive substance has a half life of 60 minutes. After 3 hours, the percentage of atom that have decayed would be

• A. 12.5%
• B. 87.5%
• C. 8.5%
• D. 25.1%

Answer 1

The correct option is B 87.5%

$N=N_0{\left(\frac{1}{2}\right)}^{\frac{t}{T_{1/2}}}$. Hence fraction of atoms decayed
$=1-\frac{N}{N_0}=1-{\left(\frac{1}{2}\right)}^{\frac{t}{T_{1/2}}}=1-{\left(\frac{1}{2}\right)}^{\frac{3\times 60}{60}}=\frac{7}{8}$
In percentage it is $\frac{7}{8}\times 100=87.5\%$