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Question

If N0 active nuclei become No16 in 80 days. Find the half-life of nuclei?


A

40 days

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B

20 days

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C

60 days

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D

30 days

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Solution

The correct option is B

20 days


Step 1: Use the radioactive formula

The activity of radioactive substance at any time t is given by

N=N0eλt

Given that NN0=116attimet=80days
116=e80λe40λ=16λ=1n(16)80

We know that:

t12=ln(2)λ

Step 2: After putting the value of λ in the above equation

t12=ln(2)ln(16)×80t12=20days

Final Answer: Hence, the correct answer is option (B).


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