Solutions: Radioactivity Questions
Q2.
(a)
(i) What is meant by the random nature of radioactive decay?
Which atom decays
at what time is pure chance![](../../../graphics/symbols/nuclides/ticksmall.png)
(ii) Explain what is meant by each of the following:
( 6 marks)
(b) The radioactive isotope of iodine 131I has a half-life of 8.04 days. Calculate
(i) the decay constant of 131I,
![](extract_halflife.png)
(8.04 x 24 x 602) = ln 2/![](../../../graphics/symbols/lamda_red.png)
= ln 2/ (8.04 x 24 x 602)
= 1.0 x 10-6 s-1 ![](../../../graphics/symbols/nuclides/ticksmall.png)
(ii) the number of atoms of 131I necessary to produce a sample with an activity of 5.0 × 104 disintegrations s–1 (Bq),
![](extract_decay.png)
5.0 × 104 = -
x N
N = - 5.0 × 104/
N = - 5.0 × 104/(answer to part (i))![](../../../graphics/symbols/nuclides/ticksmall.png)
N = - 5.0 × 104/1.0 x 10-6
N = 5.0 x 1010
(iii) the time taken, in hours, for the activity of the same sample of 131I to fall from 5.4 × 104 disintegrations s–1 to 5.0 × 104 disintegrations s–1
![](extract_decay.png)
![](extract_activity.png)
![](equationA.png)
![](equationB.png)
![](equationc.png)
ln (5.0 × 104/ 5.4 × 104) = -
t
- 0.077 = -1.0 x 10-6t
t = 0.077/1.0 x 10-6 = 7.7 x 104s![](../../../graphics/symbols/nuclides/ticksmall.png)
7.7 x 104/602 = 21 hours ![](../../../graphics/symbols/nuclides/ticksmall.png)
(6 marks)
(Total 12 marks)