Question

The half-lives in two different samples, A and B, of radioactive nuclei are related according to

T_1/2,B =

1

4

T_1/2,A.

In a certain period the number of radioactive nuclei in sample A decreases to one-eighth the number present initially. In this same period the number of radioactive nuclei in sample B decreases to a fraction f of the number present initially. Find f.

Answer 1

Given:-

T_{1/2 B} / T_1/2A=1/4

Let at a certain period the number of radioactive nuclei in sample A decreases to one-eighth the number present initially.

For sample A

No- No/8= No*e^-λt_A

1-1/8= e^-λt_A

8/7=e^-λt_A

7/8= e^λt_A

Taking logarithm we get t_A=0.0252/λ--------------------1

For sample B

No- No/f= No*e^-λt_B

1-1/f= e^-λt_B

f-1/f=e^-λt_B

f/f-1= e^λt_B

Taking logarithm we get t_B=log[ f/ f-1] /2.303*λ----------------------------2

Equation 1/ Equation 2 gives

4= 0.0580/ log[ f/ f-1]

f / [f-1]= 1.04

we get f= 26