The count rate of nuclear radiation coming from a radioactive sample containing `I^128` varies with time as follows.
Time t (minute): 0 25 50 75 100
Count rate `R(10^9 s^(-1))`: 30 16 8.0 3.8 2.0
(a) plot `In (R_0//R)`against t. (b) From the slope of the best straight line through the points,Find the decay constant `lambda`.(c ) Calculate the half-life `t_(1//2)`.

Answer

A, B, C

Explanation

(a) Here we should take `R_(0)` at time `t_(0)`
`= 30 xx 10^(9) s^(-1)`
`:. (i) In (R_(0)/R) = In ((30 xx 10^(9))/(30 xx 10^(9))) = 0`
(ii)` In (R_0/R_2) = In ((30 xx 10^(9))/(16xx 10^(9))) = 0.63`
(iii) In (R_(0)/R_3) = In ((30 xx 10^(9))/(8 xx 10^(9))) = 1.35`
(iv) `In (R_0/R_4) = In ((30 xx 10^(9))/(3.8 xx (10^9))) = 2.06`
(v) `In (R_0/R_5) = In ((30 xx (10^9))/(2 xx (10^9))) = 2.7`
(b) `:. The decay constant lambda = 0.028 min -1`
`:. The half life period `
`t_(1/2) = (0.693/lambda)`
`= (0.693/0.028) = 25 min` .