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GEIGER-MULLER COUNTER (I)
Introduction
A typical G.M. tube consists essentially of a cylindrical cathode in
the form of a graphite coating on the inner wall of a glass envelope
and an anode in the form of fine tungsten wire which stretches within
and along the axis of the tube. Usually it is filled with a mixture of
an inert gas (argon or neon) at a partial pressure of about 100 torr
and a quenching gas (halogens or organic vapours) at about 10 torr. To
allow 1onis1ng particles to enter the tube, a window covered with a
thin sheet of mica is provided at one end of a tube.
In operation, a sufficiently large potential difference i.e. applied
across the anode and cathode of the tube so that a high radial electric
field
near
the
central
wire
is
obtained.
Under
this
condition,
electrons produced by ionizing collisions between a high-speed particle
entering the tube and the inert gas atoms are accelerated towards the
anode wire by the strong electric field and acquire within a very short
distance a high speed of their own. Because of this speed, they too can
ionize other atoms and free more electrons. This multiplication of
charges repeats itself in rapid succession producing within a very
short interval of time an avalanche of electrons.
The electron avalanche is concentrated near the central wire while the
positive ions, being much heavier, drift slowly toward the cathode. For
a G.M. tube with a cathode of radius 1cm, the time of flight of the
positive ions is roughly about 100 microseconds, which is about 100
times
longer
than
the
time
necessary
to
build
up
the
electron
avalanche. The consequence of this is that after the initiation of an
electron avalanche by an entering particle the slowly moving positive
ion sheath around the anode wire increases the effective radius of the
anodes. The electric field round the wire therefore drops to a value
below that which is capable of supporting ionization by collision. The
electron avalanche ceases and a pulse of current due to this avalanche
is subsequently produced.
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The
object
of
the
counter
is
to
produce
particle entering the tube. This
a
single
pulse
for
each
can only be achieved if spurious
pulses due to secondary electrons released from the cathode surface by
the bombardment of ions are completely suppressed so that the tube can
recover as quickly as possible to be in a state when it is able to
record the next entering particle. A quenching gas (it must be both
polyatomic and of low ionization potential) introduced into the tube is
to serve this purpose. The idea is to allow the inert gas ions on their
way to the cathode to collide with the heavy molecules thereby transfer
their charges to the molecules and become neutralized - a process known
as quenching. The
cathode
and
on
molecular ions
reaching
there,
thus produced move slowly to the
capture
electrons
from
the
cathode
surface to become neutral molecules. Any excess energy that the neutral
molecules have will cause them to dissociate into individual atoms
rather than be imparted to the cathode to produce fresh electrons that
would take part in further ionizing collisions.
The usual G.M. counter circuit is as shown in the following block
diagram:
where R, a register of several M , is connected in series with the
stabilized H.T. supply and the tube. The current pulse initiated in the
tube by an entering particle produces a voltage pulse across this
resistor. The output pulse is then fed via a capacitor C to a pulse
amplifier,
which
is
followed
by
an
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electronic
scaling
unit
for
recording the number of pulses. The register is usually composed of
decade
counting
tubes.
Sometimes,
in
additional
to
decade
counting
tubes, mechanical registers are also used.
Typically, the counting rate of a G.M. counter depends on the applied
voltage. Below a minimum voltage, the threshold voltage, no counts will
be registered. This minimum voltage is a function of the gas pressure
and the anode diameter, and may be between 300V and 900V. As the
voltage is increased, more and more counts are registered. Over a range
of voltages, called the plateau range, the counting rate is relatively
insensitive to applied voltage. The change in counting rate over a 100V
range of applied voltage may be as little as 5V. Organic quenched tubes
usually have a flatter plateau than halogen quenched tubes. For still
higher applied voltages the tube may go into continuous discharge. It
is
particularly
important
that
an
organic-quenched
tube
not
be
permitted to go into continuous discharge, as the quenching gas may be
exhausted in this way.
In
this
experiment
a
counter,
which
incorporates
all
the
decade
necessary components, described above in one single unit is provided.
The G. M. tube connected to the decade counter is of type Mullard
MX168. It has a mica window and uses halogens as quenching gas.
Students are advised to do additional reading and answer the following
questions:
(i) Would the counter perform its normal duty if the polarities of the
central wire and the inner wall of the tube were interchanged?
(ii) Is there any advantage
of using halogens rather than organic
vapours as quenching gases? Explain.
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Experiment
(a) G.M. Tube Characteristics
Using handling forceps, place the radium source on the lowest shelf of
the lead castle directly below the window of the G.M. tube. Switch on
the counter and allow it to warm up for a couple of minutes. Increase
the applied voltage from 320V in steps of 10V up to 450V. At each
setting, note down the number of counts over a period of 2 minutes.
Plot a graph of count rate per minute against the applied voltage.
Indicate on your graph the plateau, the Geiger threshold voltage and
the operating voltage (i.e. the voltage at the middle of the plateau).
(b) Background Count
Remove all radioactive sources from the vicinity of the G.M. tube. Set
the
counter
voltage
at
the
operating
voltage
and
take
a
5-minute
background count.
Note: The background count rate per minute should be subtracted from
all counts in subsequent experiments in order to obtain the true count
rates due to radioactive sources alone.
(c) The Resolution Time of a G.M. Counter
After a pulse is registered, a sheath of positive ions that gradually
increases in radius remains about the anode wire. This effectively
decreases the potential gradient near the wire and not until this space
charge has drifted sufficiently far from the anode will the counter
become sensitive again. The total time taken for the tube to recover to
its
fully
sensitive
state
to
give
resolution time.
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the
next
pulse,
is
called
the
For a tube having a resolution time t, it means that for each single
count registered. The tube is inoperative for t sec. Thus if we have n
record sounds registered per sec., the lost time in one sec is nt and
the effective operating time is
1 nt 
sec. Following from this, if we
assume that the corrected count rate is N counts per sec. Then
N
1
n
1  nt 
The resolution time can be found readily using the "two-source" method.
This is carried out experimentally by counting the two sources one at a
time and then both together. If n1 , n2 , ns are the counts registered per
minute for the first source, the second source and the combination of
the two sources respectively, we can write:
and
N1 
n1
1  n1 t 
2
N2 
n2
1  n 2 t 
3
Ns 
ns
1  ns t 
4
Since N s  N1  N 2
which follows
Ns 
From
n1
n2

1  n1 t  1  n 2 t 
4 ,
we have
ns 
Ns
1  N s t 
Substituting
ns 
5
5
6
into
6 ,
we obtain after manipulating:
n 1  n 2  2n 1n 2 t
1  n1n 2 t 2
7 
Normally n 1n 2 t 2 1 , we can approximate
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7 
to
ns  n1  n2  2n1n2 t
which yields
t
n1  n 2  n s
2n 1 n 2
8
Using forceps, place a radium source left of center on the bottom shelf
of the lead castle. Then add another radium source symmetrically to the
right of center on the same shaft and finally remove the first source
without disturbing the second source. At each of these stages make a
two-minute count. Correct all the observed counts for background and
calculate the resolution time of the counter.
(d) Verification of Inverse Square Law
Remove the G.M. tube from the lead castle and attach it horizontally to
a stand provided. Using forceps, a place a radium source
5C
on
another stand and align it until its active face faces the tube window
and lies along the axis of the tube. Starting with a separation d
between the window and the source equal to 10cm and thereafter increase
d successively by 10cm until it reaches 70cm, note down the number of
counts per minute at each setting.
Correct the observed counts for background and resolution time using
equation (1), and hence plot the corrected count rate against
1
d2
to
verify the inverse square law.
Repeat
226
the
above
experiment
with
60
Co  source
in
place
of
the
Ra  source . On the same graph paper, give a plot of the inverse-square
law for the
60
Co  source and hence from the gradients of the two linear
plots deduce the strength of
60
Co  source .
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(e) Attenuation of   ray by Matter
The attenuation of a beam of   rays passing through matter depends on
photoelectric absorption, Compton scattering and pail production. The
relative importance of each of these processes, in any given case, is a
function of the initial energy of the  -photons and the atomic weight
of the absorbing material. Experimentally it has been found that the
attenuation follows closely the exponential law i.e. I is the initial
intensity of the   rays , then after transversing a layer of matter of
thickness  , its intensity I is reduced to
I  Ioe

where  is known as the linear absorption coefficient of the matter.
The value of  when the initial intensity is reduced to half is called
the half value layer (HVL).
Note that in experiments using a G.M. counter, I is proportional to N
(the counting rate corrected for background and resolution time), hence
N  N o e  
Place the
60
Co  source at a distance of about 20cm from the window of the
G.M. tube. Take a one-minute count to determine the initial count rate.
Without disturbing the setup, take a series of one-minute counts as a
succession
of
aluminum
sheets
is
placed
vertically
in
the
region
between the G.M. tube and the source using the data obtained, plot a
suitable graph and hence deduce the μ and HVL for
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60
Co  source .
References
(1) J.B.A. England, Techniques in Nuclear Structure Physics,
Part 1, Chapter 1.
(2) W.E. Burcham, Nuclear Physics An Introduction,
Second Edition, Chapter 6.
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Appendix A
Proper Handling of Radioactive Source
Source to be handled by spincer only
and and face downwards or away from
people
Source in the proper storage box.
Source Face
Use pincer to remove source from
storage
box
Picture of radioactive source. Do not face
radioactive source towards yourself or
anybody. Source must be put back into
proper storage box after use.
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