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Question: If 20 gm of a radioactive substance due to radioactive decay reduces to 10 gm in 4 minutes, then in ...

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.

A

In 8 minutes

B

In 12 minutes

C

In 16 minutes

D

In 20 minutes

Answer

In 12 minutes

Explanation

Solution

20 gm substance reduces to 10 gm (i.e. becomes half in 4 min. So T1/2=4minT_{1/2} = 4\min. Again M=M0(12)t/T1/2M = M_{0}\left( \frac{1}{2} \right)^{t/T_{1/2}}

10=80(12)t/410 = 80\left( \frac{1}{2} \right)^{t/4}18=(12)3=(12)t/4\frac{1}{8} = \left( \frac{1}{2} \right)^{3} = \left( \frac{1}{2} \right)^{t/4}⇒ t = 12 min.