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Question

Calculate the time interval between 33% decay and 67% decay if half-life of a substance is 20 minutes.


A

40 minutes

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B

20 minutes

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C

60 minutes

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D

13 minutes

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Solution

The correct option is B

20 minutes


The above question can be solved as:

Step 1:

Half life a substance =20minutes

Step 2:

Rate of decay at time t :

Nt=N0e-λt

λt=ln(No/Nt)--------(i)

Step 3:

Applying the formula of equation (ii) for 33% decay and (iii) for 67% decay:

λt2=ln(100/100-67)λt2=ln(100/33)--------(ii)

λt1=ln(100/100-33)λt1=ln(100/67)--------(iii)

Equation(ii) - Equation(iii)

λ(t2t1)=ln(0.67/0.33)=ln(2.03)ln(2)t2t1=ln2/λln2/λ=0.693/λ0.693/λ=t12t12=20min.t2t1=20min.

Therefore, the time interval between 33% decay and 67% decay is 20 minutes.


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