Question

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

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

Answer 1

Answer: (B)

87.5%

Answer 2

$N = N_{0}\left( \frac{1}{2} \right)^{\frac{t}{T_{1/2}}}.$ 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 $\frac{7}{8} \times 100 = 87.5\%$