Radioactive halftime of ^{108}Ag and
^{110}Ag
From natural silver, one can produce
the radioactive isotopes ^{108}Ag and ^{110}Ag. In this
assignment we will study the halftime of these two isotopes.
Equipment
Table
1: Equipment used
Van de Graaff generator 
GeigerMüller 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 ^{107}Ag
and ^{109}Ag 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, ^{108}Ag and ^{110}Ag.
^{107}Ag + n ^{108}Ag + g
^{109}Ag + n ^{110}Ag + g
These two isotopes will naturally
decay. This results in nuclear radiation which we can measure:
^{108}Ag ^{108}Cd + b^{}
^{110}Ag ^{110}Cd + b^{}
The beta radiation is detected by
the GeigerMüeller 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.
1.1Measurement of background
radiation
The background radiation needs to be
taken into account in order to get a correct measurement of the activity of ^{108}Ag
and ^{110}Ag. This was done by letting the detector register counts
over a longer period of time. The background radiation was measured for a total
of t_{c} = 2940 seconds, and number of
disintegrations was C = 2370.
c = C/t_{c}
c = 0.807 Bq
1.2The insecurity of m,c and (mc)
The insecurity of observed counts per second, m is given by:
The insecurity of the background
radiation, c is given by:
The total insecurity (mc) is then given by:
The insecurity of s_{c}_{ }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 GeigerMüeller tube and is counted over a 10
second period for 14 minutes. When the
GMtube 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, mc.
Table
2: Number of count
Time [s] 
Total activity (mc) [Bq] ^{108}Ag + ^{110}Ag 
S_{(mc) }[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, (mc) = 82 Bq. Furthermore
one have to take half of this value and look at what time the line has the
value (mc) = 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 ^{108}Ag and ^{110}Ag
The
half time of the isotope with the longest half life
is T_{1/2}(^{108}Ag)
= 150 +/ 10s.
1.5 Deciding the shortest halftime
The
insecurity of the activity ^{110}Ag is given by:
Time [s] 
Activity ^{110}Ag [Bq] 
Insecurity ^{110}Ag [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 ^{110}Ag
By
studying the graph one can conclude that the halftime of ^{110}Ag is
approximately 25 seconds.
1.6 Conclusion
During this experiment the halftime
of ^{108}Ag and ^{110}Ag has been determined graphically. Where
T_{1/2}(^{108}Ag) = 150 +/ 10s and T_{1/2}(^{110}Ag) = 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