First slide

Radio activity

Question

Half life of a radio-active substance is 20 minutes. The time between 20% and 80% decay will be

Moderate

A

20 minutes
B

40 minutes
C

30 minutes
D

25 minutes

Solution

We know $\frac{N}{N_{0}} = {(\frac{1}{2})}^{t / T_{1 / 2}}$
For 20% decay $\frac{N}{N_{0}} = \frac{80}{100} = {(\frac{1}{2})}^{t_{1} / 20} . . . . . . . . . (i)$
For 80% decay $\frac{N}{N_{0}} = \frac{20}{100} = {(\frac{1}{2})}^{t_{2} / 20} . . . . . . . . . (ii)$
Dividing (ii) by (i)
$\frac{1}{4} = {(\frac{1}{2})}^{\frac{(t_{2} - t_{1})}{20}};$ on solving we get $t_{2} - t_{1} = 40 \min .$

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