A radioactive substance has a half life of 60 minutes. After 3 hours, the percen

Question

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

Options:

A . 12.5%

B . 87.5%

C . 8.5%

D . 25.1%

Answer: Option B
:
B

N = N_{0} {(\frac{1}{2})}^{\frac{t}{T_{1 / 2}}}

. Hence fraction of atoms decayed

= 1 - \frac{N}{N_{0}} = 1 - {(\frac{1}{2})}^{\frac{t}{T_{1 / 2}}} = 1 - {(\frac{1}{2})}^{\frac{3 \times 60}{60}} = \frac{7}{8}

In percentage it is

\frac{7}{8} \times 100 = 87.5 %

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