A radiation detector is placed close to a radioactive source. The detector does not surround the source.

Question 22

(a) A radiation detector is placed close to a radioactive source. The detector does not surround the source.

 

Radiation is emitted in all directions and, as a result, the activity of the source and the measured count rate are different.

 

Suggest two other reasons why the activity and the measured count rate may be different. [2]

 

 

(b) The variation with time t of the measured count rate in (a) is shown in Fig. 12.1.

Fig. 12.1

 

(i) State the feature of Fig. 12.1 that indicates the random nature of radioactive decay. [1]

 

(ii) Use Fig. 12.1 to determine the half-life of the radioactive isotope in the source. [4]

 

 

(c) The readings in (b) were obtained at room temperature.

A second sample of this isotope is heated to a temperature of 500 °C.

The initial count rate at time t = 0 is the same as that in (b).

The variation with time t of the measured count rate from the heated source is determined.

 

State, with a reason, the difference, if any, in

1. the half-life,

2. the measured count rate for any specific time.

[3]

 [Total: 10]

 

 

 

Reference: Past Exam Paper – November 2017 Paper 41 & 43 Q12

 

 

 

Solution:

(a)

Any two points

emission from radioactive daughter products

self-absorption in source

absorption in air before reaching detector

detector not sensitive to all radiations

window of detector may absorb some radiation

dead-time of counter

background radiation

 

 

(b)

(i)

The curve is not smooth.

 

(ii)

clear evidence of allowance for background

half-life determined at least twice

half-life = 1.5 hours

 

 

{As the time increases, the curve should tend towards zero. However, it is observed from the graph, that the curve tends towards a count rate of 10. So,

Background radiation = 10 counts / min

This value should be reduced from the count rate at different times.

 

In 1 half-life, the count rate should be halved (after accounting for the background radiation).

 

1^st set of data:

From graph, when count rate = 160, time = 0.2 hour

This corresponds for a count rate of (160 – 10 =) 150 for the radioactive isotope only.

After 1 half-life, this value would be halved (= 150 / 2 = 75). In the graph (after adding the background radiation), the count rate would be (75 + 10 =) 85.

From graph, when count rate = 85, time = 1.7 hour

Half-life = 1.7 – 0.2 = 1.5 hour

 

2^nd set of data:

From graph, when count rate = 100, time = 1.3 hour

This corresponds for a count rate of (100 – 10 =) 90 for the radioactive isotope only.

After 1 half-life, this value would be halved (= 90 / 2 = 45). In the graph (after adding the background radiation), the count rate would be (45 + 10 =) 55.

From graph, when count rate = 55, time = 2.8 hour

Half-life = 2.8 – 1.3 = 1.5 hour

 

Averaging the 2 values give a half-life of 1.5 hour.}

 

 

(c)

1. There is no change in the half-life because the decay is spontaneous/independent of environment

 

2. The count rate (is likely to be or could be) different