Question

The count rate of nuclear radiation coming from a radiation coming from a radioactive sample containing ¹²⁸I varies with time as follows.

Time t (minute):	0	25	50	75	100
Ctount rate R (109 s−1):	30	16	8.0	3.8	2.0

(a) Plot In (R₀/R) against t. (b) From the slope of the best straight line through the points, find the decay constant λ. (c) Calculate the half-life t_1/2.

Answer 1

(a) For t = 0,

`"In" (R_0/R) = "In" ((30 xx 10^9)/(30 xx 10^9)) = 0`

For t = 25 s,

 `"In" (R_0/R_2) = "In" ((30 xx 10^9)/(16 xx 10^9)) = 0.63`

For t = 50 s,

`"In" (R_0/R_3) = "In" ((30 xx 10^9)/(8 xx 10^9)) = 1.35`

For t = 75 s,

`"In" (R_0/R_4) = "In" ((30 xx 10^9)/(3.8 xx 10^9)) = 2.06`

For t = 100 s,

`"In" (R_0/R_5) = "In" ((30 xx 10^9)/(2 xx 10^9)) = 2.7`

The required graph is shown below.

(b) Slope of the graph = 0.028
∴ Decay constant,  `lambda` = 0.028 `"min"^-1`

The half-life period (`T_"1/2"`) is given by

`T_"1/2" = 0.693/lambda`

= `0.693/0.028 = 25  "min"`