Radioactive 222Rn daughter isotopes on a paper strip
L Peralta1, T Paiva2 and C Ortigão1
1
Faculdade de Ciências da Universidade Lisboa and Laboratório de Instrumentação e
Partículas, Edifício C8, Campo Grande, 1749-016 Lisboa, Portugal
2
Escola Secundária Prof. Reynaldo Santos, Vila Franca de Xira, Portugal
Abstract
The isotope 222Rn belongs to the 238U decay chain and can be obtained from natural
mineral sources. The fact radon is a gas and its isotope daughters get implanted to the
surrounding materials, allow a set of different experiments in radiation physics. These
experiments spans from isotope decay time measurement to alpha, beta and gamma
spectroscopy. To solve the radioactive decay chain equations a simple iterative method
is used as an alternative to the exact analytical solution.
1. Introduction
The 238U is a very long-lived isotope (half-life T1 / 2 ≈ 4.47 × 10 9 y [1]), which can be
worldwide found in several minerals. The 222Rn is one of the 238U descendents. As a
noble gas, radon does not chemically react with the surrounding materials, and if it has
the chance, will escape to the atmosphere. With a half-life of 3.82 d, 222Rn is an alpha
particle emitter, and in average is estimated to be responsible for about 50% of the
natural radiation dose that living species are submitted to [2,3]. There is now a general
concern [4-8] about the effects of this radioactive isotope on health, and thus the study
of its properties is an interesting issue, both at high school and university courses. The
present work proposes a set of experiments that exploits several aspects of radiation
physics spanning from isotope decay time measurement to alpha, beta and gamma
spectroscopy. Depending on the experiment, the required equipment range from a
simple Geiger detector to a spectroscopy set-up. From the teaching point of view these
topics offer a complete set of different laboratory techniques.
2. The decay chain
The 238U decay chain is one of the natural occurring radioactive families. The 222Rn is a
direct descendent of the 226Ra and decays by alpha emission with a half-life of 3.82
days. The 226Ra descendents, as shown in the scheme below, have rather small half-lives
up to the 210Pb, making their half-life easy to follow in a laboratory classroom.
Submitted to European Journal of Physics
1600 y
3.82 d
L→ 226 Ra → 222 Rn → 218 Po
α
α
3.10 min
→
α
214
Pb
26.8min
→
β
214
19.9 min
Bi
→
β
214
164 µs
22.3 y
α
β
Po → 210 Pb → L
In the 222Rn alpha decay process the recoil energy of the descendent 218Po is enough to
implant the nuclei in the surrounding surfaces. This fact can be used to produce
radioactive sources containing the 222Rn daughter isotopes. As the three 222Rn
descendents, 218Po, 214Pb and 214Bi have half-lives in the several minutes range, they are
appropriate for measurement in the classroom.
3. The basic set-up
There are several minerals with a high content in uranium compounds and many
countries have uranium mines. A simple radon generator can be build using a small
amount of rocks with uranium compounds and a container. An inexpensive and rather
practical set-up was built using plastic beverage bottles (figure 1). In the used set-up
two bottles were coupled. In the first one, the small rocks were placed, and a hole was
drilled to allow the coupling with the second bottle. A Geiger counter was placed inside
this one, as far as possible from the rocks. The Geiger counter model used was an
AWARE Electronics RM60 radiation monitor, which has a computer interface allowing
for continuous data acquisition. Other Geiger counter type would also be suitable to
perform the experiments described ahead, even if manual data taking is necessary in that
case. The bottles were cut in halves, allowing the placement of all elements inside. Later
on the halves were join together and the couplings and holes were closed with silicone,
to prevent radon from leaking out.
The direct radiations from the rocks that constitute background to the radon
monitoring can be blocked using a lead absorber. Nevertheless, the low background
level obtained in our set-up configuration did not justify this care.
Paper
strips
Rocks
Geiger
Figure 1. Basic set-up draw.
Hanging from the bottle top strips of common paper or aluminium foil were
placed. These strips will accumulate 222Rn descendents and once taken out of the bottle
will serve later on as radioactive sources.
The rocks used in the present experiment are mainly granites and were collected
at the Quarta-Feira mine in Sabugal region, North-East of Portugal. The dose rate
delivered by each rock is relatively low, in the range of 5 to 30 µSv/h, measured with an
AUTOMESS 6150AD6 gamma dosimeter. Inside the bottle a number of 6 to 10 rocks
were used in the experiments. The activities obtained in each strip are well below 1µCi,
thus safe to be handled in the classroom.
4. The radon production experiment
After closing the set-up, radon starts accumulating inside the bottles. Radon is a gas
with density higher than air and will prefer to accumulate in the bottom of the bottle. In
this way, it will easily flow from one bottle to the other.
The radon change rate inside the bottle due to the 226Ra decay is given by the
equation [9]
dN = Rdt − λNdt
(1)
where R is the radon production rate (assumed to be constant) and λ the radon decay
constant. The solution of this equation is
N=
R
λ
(1 − e −λt )
(2)
and the radon activity time evolution will be
A(t ) = N (t )λ = R(1 − e − λt )
(3)
The Geiger detector inside the bottle will measure the decays of the radon and its
descendents. Since the 222Rn half-life is much greater then the half-life of its daughters
up to 214Po, it can be assumed that after some period of time secular equilibrium [9] will
be achieved. That is, after some time, all descendent activities will be equal to the 222Rn
activity and the overall activity inside the bottle will then be well described by equation
(3). This doesn't mean the measured activity is equal to the addition of the radon and
daughters activities. Three of the isotopes (222Rn, 218Po and 214Po) decay via alpha
emission while the other two (214Pb and 214Bi) decay via beta emission plus gamma
rays. The Geiger counter has different detection efficiencies for these radiations and
each contribution to the measured activity must be weighted by it. In figure 2 the
measured radon production rate (in Geiger counts per hour) is displayed. The data
behaviour is nicely described by equation (3) (solid line), where a production rate R of
41000 counts per hour was assumed, and λ is equal to the 222Rn decay constant. A
constant count rate of 3100 h-1 was added to the computed production rate to account
for the background due mainly to the rocks direct radiation. This background can be
measured by keeping the bottle opened, so that there is not a significant accumulation of
radon gas.
45000
40000
counts per hour
35000
30000
25000
20000
15000
10000
5000
0
0
50
100
150
200
250
300
350
time (h)
Figure 2. Radon production inside the bottle. The line is the expected result from
equation (3).
5. The implanted paper strips
If paper strips are placed inside the bottle, radon daughter isotopes will be implanted on
them. These strips became excellent radioactive sources for experiments in the
classroom. Since the 222Rn daughter isotopes have half-lives in the minutes range, there
are no problems with the disposal of the paper strips. After 1 to 2 hours the present
radioactivity is virtually zero and the strips can be put away. A wide set of different
experiments can be performed with these paper strips.
5.1. Measuring the decay of a paper strip
If a paper strip is taken out of the bottle and quickly place in front of a Geiger counter,
the decay curve of the 222Rn daughters may be obtained. This is not a simple decay
curve since a few radioactive isotopes are involved (218Po, 214Pb, 214Bi and 214Po) with
different half-lives. The general problem is well known and can be addressed in the
following way. Let n1, n2,..., nk be the number of k species of radioactive isotopes
belonging to the same non-branched decay chain, then [9]
dn1 = −λ1 n1 dt
L
dni = (λi −1 ni −1 − λi ni )dt
L
(4)
These set of equation, known as the Bateman equations [10] have a general
analytical solution, but in most textbooks on nuclear physics [9,11-13], they are solved
for a limited number of nuclides. A general method on solving them can be found in
[14], but an iterative and simple algorithm can also be used to solve them. One
advantage of this method is that it allows the inclusion of a production rate for each one
of the nuclides in the decay chain, which is particularly handy when solving the
production rate of more than one isotope. If each isotope species is produced with a rate
Ri due to a process external to the decay chain, the Bateman equation can be generalised
as
dn1 = ( R1 − λ1 n1 dt )
L
dni = ( Ri + λi −1 ni −1 − λi ni )dt
(5)
L
The algorithm can be work out in following way. Set the system initial
conditions: isotope activities A0i , half-lives T1i/ 2 = ln 2 / λi , and production rates Ri .
Compute the initial number of each isotope species as n0i = A0i / λi . The time units
chosen for the half-life will set the time scale. They should be chosen as "the best"
compromise between the decay chain involved half-lives.
Start the procedure at t = 0 and loop over the time in steps ∆t . The time step
must be small compared with the general isotopes half-lives. If this is not the case for
one of the isotopes, its decay will be prompt. For each time step, run over the isotope
species and use the activity definition, Ai = ni λi [9], to compute the average number of
decays for each species as ∆ni (t ) = λi ni (t − ∆t )∆t i if less then ni (t − ∆t ) or equal to
ni (t − ∆t ) otherwise. For each isotope species compute the number of particles after
this time step ni (t ) = ni (t − ∆t ) + ∆ni −1 − ∆ni + Ri ∆t
Go back to the loop beginning, until a maximum time is not reached or all particles have
not decayed.
This algorithm can be easily implemented into a programming language to solve
the four isotopes (218Po, 214Pb, 214Bi and 214Po) decay problem. As a secular equilibrium
is going to be assumed all activities are taken to be equal at starting. Activities as a
function of time are then computed and maybe compared with experimental values. If
all four isotope activities are taken together one would expect a behaviour like the one
displayed by the dashed curve in figure 3, where the initial peak is due to the rapid 218Po
decay ( T1 / 2 = 3.10 min). This is clearly not the case and the solid line, which has only
the contribution of the beta emitters, 214Pb and 214Bi to the activity, fits much better the
data. In fact the Geiger counter has bigger detection efficiency for beta particles than for
alphas, since its entrance window will stop these particles. The solid curve in figure 3
was computed using the iterative method, described before, and using the standard [1]
isotope half-lives. The computed activity was normalized to data at the first data point,
and a background of 25 counts per minute was taken into account.
1400
counts per minute
1200
1000
800
600
400
200
0
0
50
100
150
200
250
time (min)
Figure 3. Decay spectrum of a paper strip, measured with a Geiger counter. The dashed
line is the expected activity if all isotopes contribute to the measured activity, and the
full line is the contribution only due to the 214Pb, 214Bi beta decays. The computed
spectra have been normalized to the first data point.
The initial peak in the overall activity due to the 218Po decay is an interesting
characteristic, worth to be observed. The best way is then to use a detector sensible to
alpha particles. A silicon surface barrier detector (SSB) [15] is an excellent detector for
this purpose and was chosen to perform the job. The SSB detector is able to measure the
charged particles energy with good resolution and as we shall see later on, it allows for
beta/alpha separation. The drawback of this kind of set-up is its coast, since it requires a
vacuum system and some NIM electronic modules [15]. The used detector has a 150
mm2 active area and 400 µm depletion depth layer. A schematic drawing of the used
set-up is displayed in figure 4. The SSB detector is placed inside a vacuum chamber
with the radioactive source. A rotary pump is used to extract the air from the chamber.
A NIM high-voltage unit (like the Canberra 3102D) gives the bias voltage to the SSB
detector. A semiconductor detector preamplifier Canberra 2004 was used to read the
signal from the detector. The signal amplification and discrimination was done using
standard NIM units like the Ortec 575A and 550A respectively. The amplified signal
was sent to a multi-channel analyser (MCA) set as pulse-high analyser. The used MCA
was an Oxford PCA3 card, but most other MCA models would be suitable for this
work. In a first step, the energy spectrum of the charged particles reaching the detector
is obtained in the MCA.
High
Voltage
Pre-Amp
SSB
Amp.
Discriminator
detector
Radioactive
source
Gate
to vaccum
pump
Input
Multichannel
Analyser
Figure 4. Schematic drawing of the set-up used to measure charged particles.
The energy calibration of the system can be done using a known alpha emitter
source. In the present work a 232U source was used. This source has the advantage of
having several alpha energies ranging from 5.324 to 8.785 MeV, allowing for a precise
calibration. In order to obtain the full energy spectrum the discriminator is not
connected to the MCA gate and all signals are collected. In figure 5a. the 232U alpha
spectrum is displayed, where peaks from the 232U, 228Th, 224Ra, 220Rn, 216Po, 212Bi and
212
Po isotopes can be seen. Four out of the several peaks in this spectrum have been
chosen to perform the energy calibration. These peaks are pointed out in figure 5a) and
were chosen because they are the better resolved peaks in the spectrum. Using the peak
channel centroid as the peak position a calibration curve was obtained by fitting a
straight line to the experimental values. The experimental data and fitted curve are
displayed in figure 5b).
6000
10
5000
counts
Ra-224
Po-216
Energy (MeV)
Rn-220
4000
Po-212
3000
2000
1000
(a)
0
Po-212
8.785
8
Rn-220
6.287
6
Po-216
6.777
Ra-224
5.684
4
2
(b)
0
0
200
400
600
mca channel
800
1000
0
200
400
600
800
1000
mca channel
Figure 5. a) Charged particle energy spectrum of a 232U source. The low energy
continuum is due to electrons. b) Energy calibration curve (line) and data points
(circules). The shown numerical values are the used peak energies (in MeV) in the fit.
After the system calibration, the charged particle energy spectrum of a paper strip was
obtained (see figure 6).
1000
Po-214
100
electrons
counts
alphas
Po-218
10
1
0
1
2
3
4
5
6
7
8
Energy (MeV)
Figure 6. Charged particle energy spectrum of a paper strip source obtained with a SSB
detector. The energy scale is only meaningful for the alpha particles.
In this spectrum two different regions are clearly identified. In the low energy
the continuum spectrum is due to the detected beta particles, while in the higher energy
part the two peaks are due to the 218Po and 214Po alpha particles with 6.114 and 7.833
MeV respectively [1]. The energy calibration done with the 232U alpha source is not
applicable to the electrons in the spectrum, so the shown energy scale has no meaning
for them.
Only signals above a certain threshold were selected with the discriminator, and
the beta events were rejected. It was then possible to make a decay spectrum selecting
only decays from the 218Po and 214Po alpha emitters. In addition the MCA can be set to
the multi-channel scaling function (MCS) where the selected events are accumulated in
one channel for a predefined time (dwell time), passing the accumulation to the next
channel afterwards, and so on. A decay spectrum is then obtained. To be able to observe
the 218Po decay, the paper was taken out from the bottle as quickly as possible, a small
sample was cut, placed inside the vacuum chamber and the vacuum turned on. The
whole operation took about two minutes and the measured decay spectrum is presented
in figure 7.
160
counts per minute
140
120
100
80
60
40
20
0
-5
15
35
55
75
time (min)
Figure 7. Decay spectrum of the
theoretical expectation.
218
Po and
214
Po alpha emitters. The full line is a
In this spectrum a initial fast decrease due to the rapid 218Po decay is seen. The full line
in figure 7 is the expected result for the 218Po and 214Po alpha emitter's activity, obtained
by solving the Bateman equations with the iterative method, for the 218Po and isotope
daughters decay chain, and using tabled half-lives [1]. As explained above, a two
minutes offset between the experimental and theoretical curves was assumed. An
arbitrary normalization was use in this case, so that a general good agreement between
data and theoretical was obtained.
5.2. Gamma spectroscopy of a paper strip
Using a NaI(Tl) detector is possible to obtain the gamma spectrum from the paper strip
and identify some of the radioactive isotopes present there. Although having a limited
energy resolution these detectors are affordable by most school laboratories and easy to
maintain, making them a cost-effective choice. For this work the set-up included a
NaI(Tl) 1.5×1. in2 Canberra detector and preamplifier (2007P), NIM High-Voltage unit
(Canberra 3102D), a NIM amplifier (Canberra 2022) and a MCA (figure 8).
High
Voltage
Radioactive
source
NaI(Tl)
Detector
Pre-Amp
Amp.
Multichannel
Analyser
Figure 8. Schematic drawing of the set-up used to measure gamma photons.
The energy calibration of the MCA output was done in much the same way as described
for the alpha particles but now using standard gamma sources (60Co, 137Cs and 22Na).
The measured gamma spectrum from a paper strip is presented in figure 9. The
background is relatively low, of the order 2 to 5% under the peaks. In this spectrum it’s
easy to identify three gamma peaks (242, 295 and 352 keV) from the 214Pb and a peak at
609 keV from 214Bi. These two isotopes are in fact the main gamma emitters for this
decay chain. The huge peak in the 80 keV region is mainly due to several bismuth X-ray
emissions following the 214Pb decay, which are not resolved with this detector.
Although having lower intensity than the gamma peaks, this peak is enhanced due to
greater detector efficiency in the low energy region.
5000
4500
4000
counts
3500
3000
2500
2000
Pb-214
1500
1000
Bi-214
500
0
0
200
400
600
800
1000
1200
Energy (keV)
Figure 9. Gamma spectrum of a radioactive paper strip obtained with a NaI(Tl) detector.
6. Conclusion
222
Rn and its radioactive daughters can easily be produced in a simple apparatus, using
natural radioactive minerals containing uranium. The radioactive 222Rn daughters get
implanted in the surrounding materials and can be captured in paper strips, allowing the
production of inexpensive radioactive sources. Several experiments were performed
with these radioactive strips demonstrating that several aspects of radiation physics can
be explored with this apparatus. A simple iterative method was introduced to solve the
decay chain equations. The algorithm is easy to implement by the students, using a
programming language, and solve the equations for an arbitrary number of isotopes in
the decay chain, even if a constant production rate is introduced for some (or all) of
them.
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