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Radioactive halftime of 108Ag and 110Ag

From natural silver, one can produce the radioactive isotopes 108Ag and 110Ag. In this assignment we will study the halftime of these two isotopes.

Equipment

Table 1: Equipment used

 Van de Graaff generator Geiger-Müller tube Frequency counter Coaxial cable

Van de Graaff generator is a particle generator located on Physical institute, UiB. In this experiment a silverfoil consisting the natural silver isotopes 107Ag and 109Ag was activated by using the Van de Graaff generator. The silverfoil was irradiated by neutrons. Since the cross section of reaction is higher with thermal neutrons, we have to slow them down. This is done by placing the silverfoil in between two paraffine blocks. From this we get the two radioactive silver isotopes, 108Ag and 110Ag.

107Ag + n 108Ag + g

109Ag + n 110Ag + g

These two isotopes will naturally decay. This results in nuclear radiation which we can measure:

108Ag 108Cd + b-

110Ag 110Cd + b-

The beta radiation is detected by the Geiger-Müeller tube which further transmits signal to the frequency counter. The frequency counter gives us the number of detection which is done over a time period of 10 seconds.

The background radiation needs to be taken into account in order to get a correct measurement of the activity of 108Ag and 110Ag. This was done by letting the detector register counts over a longer period of time. The background radiation was measured for a total of tc = 2940 seconds, and number of disintegrations was C = 2370.

c = C/tc

c = 0.807 Bq

1.2The insecurity of m,c and (m-c)

The insecurity of observed counts per second, m is given by:

The insecurity of the background radiation, c is given by:

The total insecurity (m-c) is then given by:

The insecurity of sc is constant because the background radiation is only measured once. Meanwhile, the insecurity of m will vary for every value.

1.3 Measurement of the activated silver foil

The silver foil is placed underneath the Geiger-Müeller tube and is counted over a 10 second period for 14 minutes.  When the GM-tube detects a disintegration, it is discharged and wont be able to detect a new disintegration for a short period of time. Therefore we need to take the downtime, t into account. To correct the number of disintegrations the following formula is used:

m is then the observed disintegrations per second.

N is the number of counts

t is the time interval where N is measured

To correct the number of disintegrations according to the background radiation, one simply subtract the background activity from the activity m, m-c.

Table 2: Number of count

 Time [s] Total activity  (m-c) [Bq] 108Ag + 110Ag S(m-c) [Bq] 5 349 6 15 276 5 25 231 5 35 196 5 45 159 4 55 132 4 65 124 4 75 103 3 85 85 3 95 75 3 105 72 3 … …. 740 3 0.3 780 2 0.3 820 2 0.3

1.4 Deciding the longest halftime

After 115 seconds the graph enters a new linear line. One can assume that the activity of the isotope with the shortest half time is negligible. We look at where this linear line crosses x=0, (m-c) = 82 Bq. Furthermore one have to take half of this value and look at what time the line has the value (m-c) = 41Bq. At this point the activity is half of the original value, which gives us the information we need to read off the halftime from the graph.

Figure 1: Graph illustrating the total activity of 108Ag and 110Ag

The half time of the isotope with the longest half life is T1/2(108Ag) = 150 +/- 10s.

1.5 Deciding the shortest halftime

The insecurity of the activity 110Ag is given by:

 Time [s] Activity  110Ag [Bq] Insecurity 110Ag [Bq] 5 269 16 15 200 15 25 157 15 35 126 14 45 92 13 55 67 13

Figure 2: Graph illustrating the activity of  110Ag

By studying the graph one can conclude that the halftime of 110Ag is approximately 25 seconds.

1.6 Conclusion

During this experiment the halftime of 108Ag and 110Ag has been determined graphically. Where T1/2(108Ag) = 150 +/- 10s and T1/2(110Ag) = 25 +/- 5s.  It is important to emphasize that there are multiple sources of error when reading values of a graph. Human mistake it is crucial and hard to set a exact value.

Referanser

[1] A. Erdal “Phys 114 - Oppgave 7 - Måling av Radioaktiv halveringstid”, UiB, Bergen, 2019