First slide

Radio activity

Question

If 20 gm of a radioactive substance due to radioactive decay reduces to 10 gm in 4 minutes, then in what time 80 gm of the same substance will reduce to 10 gm?

Moderate

A

8 minutes
B

12 minutes
C

16 minutes
D

20 minutes

Solution

20 gm substance reduces to 10gm (i.e., becomes half in 4 min. So $T_{1 / 2}$ =4 min. Again $M = M_{0} {(\frac{1}{2})}^{t / T_{1 / 2}}$
$\Rightarrow 10 = 80 {(\frac{1}{2})}^{t / 4} \Rightarrow \frac{1}{8} = {(\frac{1}{2})}^{3} = {(\frac{1}{2})}^{t / 4} \Rightarrow t = 12 \min .$

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