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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 t1/2.
Solution
(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"`
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