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Question

Calculate the time required to decay a 15/16 of the radioactive element if half life of the element is 1600 years.

A
1000 years
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B
1500 years
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C
1600 years
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D
3200 years
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E
6400 years
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Solution

The correct option is C 6400 years
Let the initial amount of radioactive element =N0
The remaining amount after decay at time t is N=N0N0(15/16)=N0/16
From law of radio activity, N=N0eλt where decay constant, λ=ln2/t1/2=ln2/1600
So, eλt=N0/N=16
Take ln from sides, λt=ln16=4ln2
or t=4ln2ln2/1600=6400 years

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