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Question

The half-life of a radioactive substance is 30 minutes. The time (in minutes) taken between 40% decay and 85% decay of the same radioactive substance is
  1. 60
  2. 15
  3. 30
  4. 45


Solution

The correct option is A 60
We know that, N=N0eλt
For 40% decay,
N1=N0(40100)N0=(35)N0=0.6N0 
For 85% decay,
N2=N0(85100)N0=(320)N0=0.15N0
 
N2N1=(12)2
So, two half life has passed.
Since the half-life is 30 minutes, time taken for decay from 40% to 85% will be 2t1/2=2×30=60 minutes

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