Solutions: Radioactivity Questions
Q8. The radioactive isotope of sodium
has a half life of 2.6 years.
A particular sample of this isotope has an initial activity of 5.5 × 105 Bq (disintegrations per second).
(a) Explain what is meant by the random nature of radioactive decay.
.
There is equal probability of any nucleus decaying, it cannot be known which particular nucleus will decay next. ![](../../../graphics/symbols/nuclides/ticksmall.png)
The rate of decay is unaffected by the surrounding conditions, ![](../../../graphics/symbols/nuclides/ticksmall.png)
It cannot be known at what time a particular nucleus will decay, it is only possible to estimate the proportion of nuclei decaying in the next time interval. ![](../../../graphics/symbols/nuclides/ticksmall.png)
(2 marks MAX)
(b) On the axes below, sketch a graph of the activity of the sample of sodium over a period of 6 years.
![](graph7ANS.png)
Marks awarded for a continuous curve starting at 5.5 × 105 Bq plus correct 1st half-life (2.6 yrs, 2.75 × 105 Bq
correct 2nd half-life (5.2 years, 1.4 × 105 Bq) ![](../../../graphics/symbols/nuclides/ticksmall.png)
(2 marks)
(c) Calculate
(i) the decay constant, in s–1, of
,
1 year = 3.15 × 107 s
![](extract_halflife.png)
= ln 2/(2.6 x 3.15 × 107) = 8.5 × 10–9
s–1 ![](../../../graphics/symbols/nuclides/ticksmall.png)
(ii) the number of atoms of in the sample initially,
![](extract_decay.png)
Initial decay rate =
N0/
t = 5.5 × 105 Bq ![](../../../graphics/symbols/nuclides/ticksmall.png)
N =5.5 × 105/ 8.5 × 10–9
= 6.5 × 1013 (atoms) ![](../../../graphics/symbols/nuclides/ticksmall.png)
(iii) the time taken, in s, for the activity of the sample to fall from 1.0 × 105 Bq to 0.75 × 105 Bq.
![](extract_decay.png)
![](extract_activity.png)
![](equationA.png)
![](equationB.png)
![](equationc.png)
ln(0.75 × 105 /1.0 × 105 ) = - 8.5 × 10–9 x t![](../../../graphics/symbols/nuclides/ticksmall.png)
t = - (ln 0.75)/8.5 × 10–9
= 3.4 × 107 s ![](../../../graphics/symbols/nuclides/ticksmall.png)
(6 marks)
(Total 10 marks)