The half-life of a radioactive substance is 30 minutes. The time (in minutes) taken between 40% decay of the same radioactive substance is :
15
45
22
30
A
22
B
15
C
45
D
30
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Solution
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We know that, N=N0e−λt
Here, remaining amount:
N=N0−(40100)N0=(35)N0
N0N=53 and decay constant λ=ln2t1/2=ln230
Thus, N0N=eλt
Taking ln,
ln(N0/N)=λt
t=ln(N0/N)λ=ln(5/3)(ln2)/30
∴t=0.510.693/30=22min
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